Experiment Instructions

HM 112 Fluid Mechanics

Trainer
 DTP_10
05/2016

HM 112 FLUID MECHANICS TRAINER

All Rights Reserved G.U.N.T. Gerätebau GmbH, Barsbüttel, Germany 05/2016

Experiment Instructions
Last modification by: Dipl.-Ing. Peter Mittasch

Please read and follow the safety regulations before the first installation!

Publication-no.: 917.000 00 A 112 02 (A) DTP_10

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Table of Contents
1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

2 Device description. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

2.1 Experimental unit layout . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

2.2 Experimental unit equipment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
2.2.1 Fixed pipe sections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
2.2.2 Measuring objects. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
2.3 Experimental unit function . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
2.4 PC data acquisition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

3 Safety . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

3.1 Work safety . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

3.2 Operating safety . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

4 Software . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

4.1 Hardware and software installation . . . . . . . . . . . . . . . . . . . . . . . . . 11

4.2 Starting the software . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
4.2.1 The “system diagram” window . . . . . . . . . . . . . . . . . . . . . . 13
4.2.2 The “measurement diagram” window . . . . . . . . . . . . . . . . . 14
4.2.3 Menu bar structure and commands . . . . . . . . . . . . . . . . . . 16
4.2.4 The “Venturi Nozzle” window . . . . . . . . . . . . . . . . . . . . . . . 18

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5 Experimental method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

5.1 Leak test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

5.2 Two tube manometer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
5.2.1 Differential pressure measurement. . . . . . . . . . . . . . . . . . . 23
5.2.2 Absolute pressure calculation . . . . . . . . . . . . . . . . . . . . . . . 24
5.3 Manometer connection and operation . . . . . . . . . . . . . . . . . . . . . . . 25
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5.3.1 Bleeding . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
5.3.2 Adjusting the zero point . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
5.3.3 Performance of the measurement . . . . . . . . . . . . . . . . . . . 26
5.3.4 Ending the measurement . . . . . . . . . . . . . . . . . . . . . . . . . . 27
5.4 Six tube manometer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
5.5 Electronic pressure measurement. . . . . . . . . . . . . . . . . . . . . . . . . . 29

6 Experiments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31

6.1 Pipe flow with friction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31

6.1.1 Basic principles. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
6.1.2 Experimental method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
6.1.3 Comparison with calculation . . . . . . . . . . . . . . . . . . . . . . . . 35
6.2 Coefficients of resistance for special pipe components . . . . . . . . . . 37
6.3 Basic principles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
6.3.1 Pipe elbow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
6.3.2 Experimental method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
6.3.3 Calculation of coefficients of resistance . . . . . . . . . . . . . . . 40
6.3.4 Changes of cross-section . . . . . . . . . . . . . . . . . . . . . . . . . . 42
6.3.5 Experimental method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
6.4 Coefficient of resistance for pipe fittings . . . . . . . . . . . . . . . . . . . . . 44
6.4.1 Experimental method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
6.4.2 Calculation of coefficients of resistance . . . . . . . . . . . . . . . 47

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6.5 Opening characteristics of shut-off devices . . . . . . . . . . . . . . . . . . . 49

6.5.1 Experimental method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
6.5.2 Evaluation of the experiment . . . . . . . . . . . . . . . . . . . . . . . 52
6.6 Pitot tube . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
6.6.1 Experimental method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
6.6.2 Comparison with calculation . . . . . . . . . . . . . . . . . . . . . . . . 54
6.7 Volumetric flow measurement with nozzle/orifice . . . . . . . . . . . . . . 56
6.7.1 Experimental method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56
6.7.2 Comparison with calculation . . . . . . . . . . . . . . . . . . . . . . . . 57
6.8 Venturi nozzle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60
6.8.1 Experimental method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60
6.8.2 Comparison with calculation . . . . . . . . . . . . . . . . . . . . . . . . 62

7 Appendix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63

7.1 Technical data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63

7.2 Bibliography. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65
7.3 Tables and Diagrams . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65
7.4 Formulae . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69
7.5 Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72

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1 Introduction

The G.U.N.T. HM 112 Fluidmechanics Trainer

allows experiments for flow and pressure mea-
surement and determination of flow losses and
pressure characteristic for pipes and various pipe
components. The following topics can be
investigated in detail on the experimental unit:
– Various flow and pressure measuring methods
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– Function of nozzle, orifice, venturi tube, etc.

– Determination of coefficients of resistance
head losses
– Losses due to pipe bends or angles, changes
of cross-section and shut-off devices
– Measurement of opening characteristics for
shut-off devices
In addition the student gains skills in the
preparation and performance of series of
experiments, and knowledge of the use of
pressure and flow rate measuring equipment.
The experimental unit is fitted with a closed water
circuit, which means that it can be used
independently of the mains water supply. It can be
used in different locations in training, seminar and
lecture rooms.

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2 Device description

The experimental unit has the following features:

– The entire experimental set-up is clearly laid

out on a laboratory trolley.
– Four castors make the experimental unit
mobile and easy to manoeuvre
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– Closed water circuit allows operation in-

dependently of the mains water supply
– Flow rate measurement using a variable-area
flow meter with electronic position measuring
of the float
– 5 independent pressure measuring
systems for measurement of differential
pressure and head loss
– USB-Multifunction circuit board for
PC data acquisition
– Disturbance-free pressure tapping using
annular chambers
– Easy and quick connection between
measuring points and pressure gauges
using hoses with quick action couplings
– Variety of measuring objects for fluid
mechanics
– Some measuring objects transparent,
making function visible
– Seven different fixed pipe sections
– Pipe sections are interchangeable, allowing
the use of individual sections
– Easy pipe section selection using hoses
with quick action couplings

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– Standard measuring length of 1m for pipe

friction measurements

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2.1 Experimental unit layout

11 10 9 8 7 6 5

2
12
1
13

14 15 16 17 18

1 Return hose 10 Rotameter

2 Electronic pressure sensor 11 Thermometer
3 Main switch 12 reducing valve
4 Switch for pump (covered) 13 Feeding hose
5 Digital displays for pressure 14 Pump
6 Differential pressure sensor 15 Drain valve
7 Return valve 16 Various measuring sections
8 Six tube manometer 17 Water tank
9 Two tube manometer 18 Interchangeable measuring objects

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2.2 Experimental unit equipment

2.2.1 Fixed pipe sections

1 Return valve with return pipe to

water tank
2 Galvanized steel pipe, 1/2"
1 3 Cu-pipe 18 x 1
2 4 PVC-pipe 20 x 1.5
3
4 5 Cross-section contraction
PVC 20-16
6 Cross-section expansion
PVC 20 - 32
5
7 7 Section for interchangeable
6
measuring objects
8 Pipe bend, pipe angle
PVC 20 x 1.5
8
9 Self closing measuring glands
9

Fig. 2.3 Arrangement of pipe sections

2.2.2 Measuring objects

The measuring objects can be inserted into the

measuring section (7) using union nuts. The
measuring objects are fitted with annular chambers
and hose connections for pressure measurement.
– Slanted seat valve
– Membrane valve
Fig. 2.1 Pitot tube
– Ball cock
– Non-return valve
– Dirt trap with filter inserts
– Pitot tube
– Measuring orifice and nozzle
– Venturi tube
Fig. 2.2 Venturi tube

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2.3 Experimental unit function

After the pump (P), the water first off all passes the
flow rate-/ and temperature measurement (F1 &
T1) and the reducing valve (V1). If the hoses are
unplugged (6,7), the reducing valve can be used to
shut off the water supply. It is also used to adjust
the flow rate.
The water is then fed to the selected pipe
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section (1) via the feeding hose (6).

The pressure is measured at measuring glands at
the beginning and end of the measuring section.
Once the water has flowed through the pipe
section, it is fed back to the water tank via a second
hose (7).
A return valve (V2) can be used to restrict the
drain.

2 3 4 5
1 Measuring sections
2 Two tube manometer
3 Six tube manometer
4 Differential pressure sensor
5 Pressure sensors
6 Feeding hose
7 Return hose
V1 6 7 V2

B Water tank
P Pump
1
FI-01 Rotameter
TI-01 Thermometer
V1 Reducing valve
B V2 Return valve
P V3 Drain valve

V3
Fig. 2.4 Arrangement of pipe sections

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2.4 PC data acquisition

This experimental unit is equipped for PC data

acquisition. This involves the recording of differen-
tial pressure, excess pressure and flow rate by
electronic sensors. The sensors output voltage
signals from 0-10V. With the exception of the flow
rate sensor, which works with a variable resistance
at +5 V. The differential pressure (1), and the ex-
cess pressures (2) are indicated on digital displays
in the switch cabinet.

Fig. 2.5 Switch cabinet with digital displays

The signals are displayed on the PC monitor using a

visualisation program that runs under Windows TM.
The experimental unit can also be operated with-
out a PC.

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3 Safety

3.1 Work safety

Always read and observe the following

instructions!

DANGER, electric shock!

– The switch cabinet is only to be opened by
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specialist personnel
– Prior to opening the switch cabinet,
disconnect from the mains
– Protect switch cabinet and PC against
splashed water, as this can damage
components

3.2 Operating safety

CAUTION, store experimental unit in a

frost-free location!
Empty the water tank if the unit will not be used for
long periods.

CAUTION, do not overload pressure sensors!

The pressure measuring range for the sensors is
0 - 200 mbar.
– Pressures over 600 mbar or negative
pressures can damage the pressure
sensors. The volumetric flow rates must
therefore be restricted using the valves in the
inlet and the drain to ensure that this value is
not reached.
– Ensure correct polarity when connecting the
differential pressure sensor.

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4 Software

4.1 Hardware and software installation

The USB cable for the LabView TM application soft-

ware should be connected and installed in the fol-
lowing order:
– 1.Software installation
Insert CD in drive, run Setup.exe and
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follow the instructions in the dialog box

– 2. Connect the USB cable
– 3. Start the software application

4.2 Starting the software

After starting the software, the “system diagram”

window appears.
The first time you open the software, a language
selection window also appears. The language can
be changed later using the pull-down menu under
“Language” in the menu bar.
Clicking on “Start” in the menu bar allows you to
choose between the “system diagram” and “mea-
surement diagram” windows. The menu bar also
includes the “EXIT” option for exiting the program.
In the system diagram screen, you can choose the
measuring section used in the experimental setup.
Note:
The menu options are context sensitive, i.e. not all
options can be selected at all times.

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Recording measured values:

• Open the “measurement diagram” window
under “Start” in the menu bar.
• Create a new measuring series (“New
series”) under “File” in the menu bar.
• If necessary, specify the axes for the
diagram. This setting is made using “View”
and “choose axis” in the window that is
subsequently opened. You can select a
maximum of four y-axes and one x-axis.
• You can then record measured data using
the record button (Fig. 4.2, 3) or by selecting
the “take record” option under “Edit” in the
menu bar.
• After recording the measuring series, you
can save it to the hard disk or an alternative
medium using the “save series” command in
the “File” menu.

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4.2.1 The “system diagram” window

The system diagram is a clearly arranged

representation of the measuring task. The lower
button (1) can be used to toggle between different
measuring tasks.
– Pipe
– Nozzle/Orifice
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– Pitot Tube
– Pipeline Fittings
– Venturi Nozzle
Pressures can be represented as water columns
or using a differential pressure gauge. To change
the setting, use the “View” option (3) in the menu.
The flow, pressures and temperature are
displayed online (5).
The “Start” option (2) takes you to the “measure-
ment diagram” option. This window can be used to
create the diagrams.
The “Language” option (4) can be used to select
one of the four available languages.

1 5

Fig. 4.1 "System diagram" window

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4.2.2 The “measurement diagram” window

In the “measurement diagram” window, click on

“Start” in the menu bar to record, load and save a
curve.

1 2 3 4 5 6

Fig. 4.2 "Measurement diagram" window

The options in this window are only active if a

measuring series has actually been loaded or
created.

Background / Curve
Left clicking on the buttons for the background (2)
and the curve (1) allows you to set the colour of
these elements.
Measured value recording
Clicking on the button with the red spot (3) records
measured data and adds it to the active data
series.

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Cursor
The arrow buttons (5) allow the cursor to be moved
over the measuring points already recorded.
Measured values are displayed at the cursor
position.
Delete measured value
The button with the red cross (4) deletes individual
measuring points from the active data series. The
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data record at which the cursor is located will be

deleted.
Select active measuring series
In a file containing several measured data series,
this button (6) can be used to select the active
series. A file can either contain just one or several
measuring series. The number of measuring
series per file is limited to a maximum of 10.
Scaling
The scaling can be changed by left clicking directly
on the limit values.

Measured data can also be recorded and deleted

using the menu (“Edit - Take record” or “Edit -
Delete record”). The associated abscissa is dis-
played at the cursor position. Several curves can
be plotted in the diagram. A new curve is created
using the “file” command. The curve can also be
saved to a file here. The active curve can be
selected using “select curve”.

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4.2.3 Menu bar structure and commands

• Start
– measurement diagram
Opens the window containing x/y
graphs for recording, editing and saving
measuring series.
– system diagram
Opens a window in which the ex-
perimental setup and the relevant
measured values are displayed online.
– EXIT
Exits the program.
• File
– print window
Prints the window on the default printer.
– open file (measurement diagram only)
Opens a previously saved file.
– new series (measurement diagram only)
Creates a new file for at least one data
series.
The following options are only active if a data
series is loaded in the “measurement
diagram” window.
– save series
Saves a measuring series from the
working memory to a file (e.g. on the
hard disk).
– delete series
Deletes a measuring series from the
working memory.

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– save all series

Saves all measuring series from the
working memory to a file.
– delete all series
Deletes all measuring series from the
working memory.
– print Graph
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Outputs the x/y graph on the default

printer.
– print table
Outputs a table for the current measur-
ing series on the default printer.
• Edit
– take record
Adds a measuring point to the series.
– delete record
Deletes a measuring point (at the
cursor position) from the series.
• View
– choose axis (“measurement diagram”
only)
Opens a window for selecting the max.
4 y-axes and 1 x-axis.
– graph (“measurement diagram” only)
Displays the x/y graph
– table (“measurement diagram” only)
Displays the table for the measuring
series
– pressure (“system diagram” only)
Displays the differential pressure to the
ambience

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– differential pressure (“system dia-

gram” only)
Displays the differential pressure
between P1 and P2
• Language
Allows you to choose one of the four
languages
– German
– English
– French
– Spanish
• ?
– About GUNT
Information about GUNT

4.2.4 The “Venturi Nozzle” window

The “Venturi Nozzle” window represents the

pressure and speed progression along the Venturi
Nozzle. This representation clearly illustrates
Bernoulli’s Law.

Fig. 4.3 "Venturi Nozzle" window

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Basic information on the structure of the measured

data file:

Datei
File The measured data file can consist of several
Messreihe
Set of records
1 1 measuring series.
Kopf
Header Each measuring series has a separate header,
Messdatensatz 1
Record n
which is followed by the measured data records.
Messdatensatz 2 A measured data record is the data that is
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Messdatensatz
Record 3 3 recorded at a specific point in time.
Record 2 A measuring series contains the data records for
Record 1
Messdatensatz n several points in time, which are used to plot the
curves.
Messreihe
Set of records
2 2

Kopf
Header
Messdatensatz
Record n 1
Messdatensatz 2
Messdatensatz
Record 3 3
Record 2
Record 1
Messdatensatz n

.
.
.
.

Fig. 4.4 File-structure

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5 Experimental method

Before commencing the experiment:

– Place experimental unit on a flat surface and
secure against rolling away (brake).
– Fill up water tank.
– Connect to power supply.
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If you intend to work with PC data acquisition, the

following steps must also be completed:
– Connect experimental unit and data acquisi-
tion card to PC with 37-pin Sub D cable.
– Turn on experimental unit using master
switch (digital displays in switch cabinet now
show values).
– Switch on PC.
– Start Windows TM.
– Open GUNT program group
and start HM112 .

5.1 Leak test

Before starting up the experimental unit and

starting any experiments, a leak test should be
performed on the experimental unit.
The procedure for this is as follows:
– Check tightness of self closing measuring
glands and remove possible particles
– Connect pipe section to feeding and return
hose.
– Open return valve.
– Switch on pump.

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– Slowly open reducing valve and bleed pipe

section.
– Slowly increase pressure by closing the return
valve.
– Check all lines, hoses and connections for
leaks.
– Repeat procedure for all pipe sections.

5.2 Two tube manometer

The two tube manometer allows both differential

pressures and excess pressures to be measured
in mm column of water; excess pressures can be
converted into absolute pressures taking into ac-
2 count the atmospheric air pressure.
– The measuring range is 0 - 680 mm column
of water
– The manometer comprises two glass level
1 tubes (1) with a metal mm scale behind them.
– The two level tubes are connected together at
the top and have a common bleed valve (2).
– The differential pressure is measured with
the bleed valve closed and the excess
pressure with the bleed valve open.
– The measuring points are connected to the
bottom of the level tubes using quick action
hose couplings (3).
– Each level tube has a drain valve (4) at the
3 bottom.

Fig. 5.1 Two tube

manometer

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5.2.1 Differential pressure measurement

Here the bleed valve is closed. An air cushion

forms over the two columns of water with the
pL pressure pL. This means that the pressures to be
measured p1 and p2 are

p 1 = p L + h1 r g
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p 2 = pL + h 2 r g .
Dh
The differential pressure is then
h1

D p = p 1 - p 2 = p L + h1 r g - p L - h 2 r g .
h2
The pressure pL cancels out and the following is
found
p1 p2
Dp = Dh r g mit D h = h1 - h 2 .
Fig. 5.2 Differential pressure
measurement Using the pressure pL the zero point for the differential
pressure measurement can be adjusted.
For a maximum measuring range it is best to
h + h2
position the zero point or mean value 1 in the
2
h
middle of the measuring scale max
2

h1 + h 2 h max p1 - pL + p 2 - pL
= = .
2 2 2rg

The pressure of the air cushion is therefore given as

p1 + p 2 - h max r g
pL = .
2

The pressure is adjusted using the bleed valve,

see also section 5.3.2.

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5.2.2 Absolute pressure calculation

p0 To calculate the absolute pressure, the bleed

valve is opened and the excess pressure is
measured. The pressure pL corresponds to the at-
mospheric air pressure p0.
Here it is also necessary to take into account the
h
height hm between the measuring point and the
zero point on the manometer

p abs = p 0 + ( h + h m ) r g .

hm

pabs

Fig. 5.3 Absolute pressure

measurement

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5.3 Manometer connection and operation

– Connect pipe section to feeding and return

hose.
– Open return valve.
– Connect manometer to the pipe section to be
measured using connecting hoses
– Switch on pump
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5.3.1 Bleeding

– Close top bleed valve

Close
– Open both bottom drain valves
– Slowly open the reducing valve in the inlet of
the pipe section to be measured
Pipe section and connecting hoses are bled by the
powerful flow of water.

Fig. 5.4 Bleeding step 1

When no more air bubbles are visible in the

connecting hoses:
– Close return valve
– Slowly close both bottom drain valves
simultaneously. Ensure that both columns
of water rise evenly and that there is no over-
flow between the level tubes.
Simultaneously close

Fig. 5.5 Bleeding step 2

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5.3.2 Adjusting the zero point

To ensure the largest possible measuring range,

Set level here the zero point for the manometer should be in the
middle of the scale.
– Close pipe section drain, flow rate is equal to
zero.
Middle of scale – Level in the two measuring tubes is the same
– Carefully adjust level to the middle of the
scale using the bleed valve.

WARNING! Level can only be adjusted upwards

Fig. 5.4 Setting zero point using the bleed valve. If the level is too high, the
pipe network must be drained. It is then necessary
to bleed the pipe section again before a lower zero
point can be set.

5.3.3 Performance of the measurement

Set required flow rate using inlet valve. During this

process the return valve is fully open. Check this
on the flow meter digital display.
Read differential pressure as height difference
Dh between the two columns of water.
In case of fluctuating display, estimate mean
value. In the case of differential pressure
measurements, the key issue is not absolute
precision, but reproducible readings.

Fig. 5.5 Perform measurement

WARNING! At a large flow rate the differential pres-

sure can increase so much that the water overflows
through the top connecting pipe into the measuring
tube connected to the lower pressure. If necessary,

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reset the zero point (see 5.3.2) or use electronic pres-

sure sensors with a greater measuring range.
The differential pressure measurement is always
performed with the bleed valve closed.

5.3.4 Ending the measurement

– Following the conclusion of the measure-

All Rights Reserved G.U.N.T. Gerätebau GmbH, Barsbüttel, Germany 05/2016

ment, close the return valve

– Switch off pump
– Fully open reducing valve
– Open bleed valve and both drain valves.
Manometer empties and the pipe section is
depressurised.
The connecting hoses can now be disconnected
and changed.
WARNING!Close unused measuring glands with
Fig. 5.6 Finish measurement
filler plugs.

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5.4 Six tube manometer

4 2 The six tube manometer comprises six glass level

tubes (1) with a mm scale behind them.
– The measuring range is 390 mm WG.
1 – All level tubes are connected together at the
top and have a common bleed valve (2). The
measuring connections (3) are at the bottom.
– The differential pressure is measured with
the bleed valve (2 & 4) closed and the excess
pressure with the bleed valve (4) open.
The function, connection and operation are
identical to the manometer described in 5.2 & 5.3.

Fig. 5.7 Six tube manometer

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5.5 Electronic pressure measurement

2
The differential pressure unit has 2 connections,
P1 and P2 (1), between which differential pressure
up to a maximum of 200 mbar can be measured.
P1 (+) P2 (-) The higher pressure must be at P1 and the lower
pressure at P2. The valves (2) are used for
1 bleeding.
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The excess pressure measuring unit has 6

Fig. 5.8 Differential pressure
measuring unit connections (3) (P3 - P8) for excess pressure from
0 - 600 mbar. The valves (4) are used for bleeding
the measuring lines.

The procedure for bleeding the electronic pressure

measuring units is as follows:
– Open all bleed valves

4 – Connect measuring lines to required connec-

tions and the pipe section to be measured.
– Open feeding valve and return valve
– Switch on pump
– Close return valve slightly
A powerful jet of water flows through the pipe
3 section and measuring lines. Allow the water to
flow until no more air bubbles are visible in the
Fig. 5.9 Excess pressure measurement lines.
measuring unit
– Close all bleed valves
– Switch off pump

WARNING!Never open the bleed valves for un-

used connections as otherwise water can escape
from these connections.

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6 Experiments

In this section some experiments are described as

examples of the experiments that can be per-
formed with this unit. The range of experiments
makes no claim of completeness, but it is intended
to serve as a stimulus for your own experiments.
The experimental descriptions are divided into a
section on basic principles containing the most
All Rights Reserved G.U.N.T. Gerätebau GmbH, Barsbüttel, Germany 05/2016

important calculation formulae, the actual experi-

mental method with recording of the measured
values and a comparison between the calcula-
tion and the experiment.
The measured results listed should not be viewed
as reference or calibration values for all conditions.
Depending of the individual components used and
skill, smaller or larger variations can occur.

6.1 Pipe flow with friction

6.1.1 Basic principles

In these experiments, the pressure loss pv or the

head loss hv for a flow subject to friction will be
determined experimentally.
With turbulent pipe flow, where the flow is con-
sidered steady at Reynolds’ numbers of
Re > 2320, pressure loss is proportional to the
– length l of the pipe
– Coefficient of pipe friction l
– Density r of flowing medium
– Square of the flow speed v.
In addition, the pressure loss increases as the pipe
diameter reduces. It is calculated as follows

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l ×l
pv = r ×v 2

2 ×d

The associated head loss hv is calculated as follows

l ×l v 2
hv =
d 2 ×g

In the case of turbulent pipe flow (Re > 2320), the

pipe friction coefficient l depends on the pipe
roughness k and Reynolds number Re. The pipe
roughness k defines the height of the unevenness
of the wall in mm. The roughness of the experi-
mental pipes is listed in a table in the appendix.
The relationship between Re, l and k is shown in
the diagram based on Colebrook and Nikuradse.
Here, the wall roughness k is related to the pipe di-
ameter d.
Instable

limit curve

sm
oot
hp
ipe
laminar turbulent (k=
0)

Fig. 6.1 Pipe friction coefficient corresponding to Colebrook and Nikuradse

(taken from "Dubbel: Taschenbuch für den Maschinenbau") [Engineering Handbook]

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The Reynolds’ number Re is calculated from the

pipe diameter d, flow speed v and kinematic
viscosity n

vd
Re = .
n

The kinematic viscosity for water can be taken

All Rights Reserved G.U.N.T. Gerätebau GmbH, Barsbüttel, Germany 05/2016

from table 7.1 as a function of the temperature.

The flow speed v is calculated from the volumetric
flow V& and the pipe cross-section

4 V&
v = .
pd 2

For hydraulically smooth pipes (Re < 65 d/k)

and a Reynolds’ number in the range of
2320< Re < 105 the pipe friction coefficient is
calculated using the Blasius formula

0.3164
l= 4
.
Re

For pipes in the transition range to rough pipes

(65 d/k < Re < 1300 d/k, the range below the limit
curve in the diagram) the pipe friction coefficient is
calculated according to Colebrook
-2
é æ 2.51 0.27 ö ù
l = ê2 lg çç + ÷
÷ ú .
êë è Re l úû
d
k ø

It is an implicit formula that has to be iteratively

resolved. First of all estimate l, place it in the
formula and calculate an initial approximation.

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This approximation is re-used in the equation to

calculate a second approximation.
If the estimated value is taken from the Colebrook
and Nikuradse diagram, the initial approximation is
generally sufficiently accurate and the values only
differ after the 3rd decimal place.

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6.1.2 Experimental method

In this experiment, pipes made of different

materials (PVC, copper and galvanized steel) are
compared. The measuring length is 1000 mm.
The pressure gauge is connected and the measure-
ments are carried out as described in section 5.3.
The flow rate V& is stated in m3/h.
The displays on the two tube manometer or the diffe-
All Rights Reserved G.U.N.T. Gerätebau GmbH, Barsbüttel, Germany 05/2016

rential pressure sensor and rotameter are noted.

Measured results:

Volumetric flow V& Differential pressure p v Head loss hv

Pipe section
in m3/hin in mbar in mm

2 Galvanized steel, 1/2" 1.2 26 255

3 Cu 18 x 1 1.2 19 220
4 PVC 20 x 1.5 1.2 15 160

6.1.3 Comparison with calculation

Here, the measured head losses are compared with

values calculated mathematically. For the calcula-
tion, the wall roughness of the pipes used must be
known.

Wall roughness of experimental pipes

Material Surface Wall roughness k
Copper pipe, Cu Technically smooth 0.001 mm

PVC pipe Technically smooth 0.001 mm

Steel pipe, St galvanized 0.1 mm

In terms of the kinematic viscosity of the water, for a

temperature of 30°C, a value of n = 0.801× 10 -6 m 2 / s
is read from table 7.1. This data can be used to cal-
culate the head loss.

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Calculation of head loss

Internal Volumetric flow Flow Reynolds’

smooth /
Pipe section diameter speed in number d/k
d in mm V& in m3/h V& in m3/s m/s Re
rough

2 St, gal. 1/2" 16 1.2 33 × 10-5 1.66 33159 160 glatt

3 Cu 18 x 1 16 1.2 33 × 10-5 1.66 33159 16000 glatt

4 PVC 20 x 1.5 17 1.2 33 × 10-5 1.47 31199 17000 glatt

Calculated Measured
l calculation Coefficient of
Pipe section head loss head loss Variance
according to pipe friction l
hv in m hv in m
2 St, gal. 1/2" Colebrook 0.0335 0.253 0.255 + 0.78 %
3 Cu 18 x 1 Blasius 0.0234 0.217 0.220 +1.36 %
4 PVC 20 x 1.5 Blasius 0.0238 0.154 0.160 + 3.75%

Taking into account the reading accuracy of ± 1mm

column of water, the concordance between the
calculation and the experiment can be rated as
good.

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6.2 Coefficients of resistance for special pipe components

6.3 Basic principles

Special pipe components and fittings such as pipe

bends or elbows, pipe branches, changes in
cross-section or also valves and flaps produce
additional pressure losses apart from the wall
friction losses.
All Rights Reserved G.U.N.T. Gerätebau GmbH, Barsbüttel, Germany 05/2016

For changes in cross-section and the associated

changes in speed, the total pressure loss must
take account of the component from Bernoulli’s
pressure loss (dynamic pressure). The Bernoulli
equation with loss term is

r v 12 r v 22
+ p1 + r g z 1 = + p 2 + r g z 2 + Dp v .
2 2

Assuming that the heights z1 and z2 are equal, this

gives the measurable total pressure loss

r
Dp ges = p1 - p 2 = (v 22 - v 12 ) + Dpv .
2

Correspondingly, the head loss is then

1
hvges = (v 22 - v 12 ) + hv .
2g

Unlike the wall friction losses investigated in the

previous section, apart from a few special cases the
additional flow resistance cannot be calculated
exactly.
For the various elements, the literature specifies
empirically obtained coefficients of resistance z.
They can be used to easily calculate the additional
pressure losses.

v 2
pvz =zr
2

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or for the head loss

v 2
hvz =z .
2g

This means that for the total head loss,

we can state that

1 l l v 2 l l v 2 v 2
hvges = (v 22 - v 12 ) + 1 1 1 + 2 2 2 + z 2
2g 2 g d1 2 g d2 2g

The pipe friction resistance must be determined

separately for the sections before and after the
change of cross-section. By contrast, the coeffi-
cient of resistance is only related to the speed v2
after the change of cross-section.
If the speeds are equal, there is no dynamic pres-
sure component and a combined pipe friction com-
ponent is used.
The measured total head loss and the known pipe
friction can be used to determine the coefficient of
resistance z

2 hvges g é æd ö
4
ù é l æd 2 ö
4
l ù
z= - ê1 - çç 2 ÷÷ ú - êl 1 1 çç ÷÷ + l 2 2 ú.
v 22 êë è d 1 ø úû êë d 1 è d1 ø d2 ú
û

With no change of cross-section (d1/d2 = 1), the

expression is simplified

2 hvges g l
z= 2
-l .
v d

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6.3.1 Pipe elbow

For pipe elbows, the coefficient of resistance z

depends on the angle of deviation of the flow and
the ratio of the elbow radius to the pipe diameter. In
addition, the coefficient of resistance is influenced
by the shape of the elbow. For this special case of
R< d a pipe elbow with 90° deviation, the following dia-
gram is applicable for smooth pipes.
All Rights Reserved G.U.N.T. Gerätebau GmbH, Barsbüttel, Germany 05/2016

R>d For pipe angles, i.e. elbow radius less than the
Pipe bend Pipe angle Pipe knee pipe diameter (R/d<1) the coefficients of resis-
piece tance for knee pieces are approximately applica-
ble.
Fig. 6.2 Various pipe elbows

Bend

Kneepiece

Fig. 6.3 Coefficients of resistance of smooth 90° elbows (VDI Wärmeatlas 10. Aufl. 2006)

For strung-together 90° pipe elbows (offset el-

bows), as in the case of this trainer, the total resis-
tance value must be calculated using the following
formula:

z = 2 × 0.7 × z 90 ° (VDI Wärmeatlas)

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6.3.2 Experimental method

Connect double tube manometer to pipe angle

measuring glands (pipe section 8) and perform
measurement as described in section 5.3. Note
the displays on the double tube manometer or on
the differential pressure sensor and flow meter.
Repeat the measurement with the pipe bend (pipe
section 8).
Measured results:

Volumetric flow V& Differential pressure Dp vges Head loss hvges

Pipe elbow
in m3/h in mbar in mm

2 x Angle 90°
1.2 16 163
PVC 20 x 1.5
2 x Bend 90°
1.2 9 92
PVC 20 x 1.5

6.3.3 Calculation of coefficients of resistance

The measured values will be used to determine the

coefficients of resistance for the pipe angle and
bend. As no change of cross-section occurs in this
case, the simplified formula for zcan be used for
the calculation
2 hvges g l
z= 2
-l .
v d
For l, the pipe length between the measuring con-
nections related to the pipe centre line is used.

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In terms of the kinematic viscosity of the water, for a

temperature of 12°C, a value of n = 1. 227 × 10 -6 m 2 / s
is read from table 7.1.

Calculation of coefficients of resistance z for pipe angle and bend

Internal diameter

Volumetric flow

Flow speed v in

number Re
Reynolds’
All Rights Reserved G.U.N.T. Gerätebau GmbH, Barsbüttel, Germany 05/2016

Length l
in mm

m/s
d

Pipe section in d/k

mm V& in m3/h V& in m3/s

8 Angle 17 320 1.2 33 × 10-5 1.45 20090 17000

8 Bend 17 320 1.2 33 × 10-5 1.45 20090 17000

l calculation Coefficient of Measured head Coefficient of Coefficient of

Pipe section
according to pipe friction l loss hvges in m resistance z resistance z90°

8 Angle Blasius 0.0266 0.163 1.01 0,72

8 Bend Blasius 0.0266 0.092 0.35 0,25

The coefficient of resistance for one angle corre-

sponds almost with the value read from the dia-
gram (fig. 6.3) for pipe knee piece (z = 0.78).

The coefficient of resistance for the bend corre-

sponds with the value read from the diagram
(fig. 6.3) of z = 0.25 (for r/di = 2.26 - the ratio is actu-
ally at R/d = 2.35).

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6.3.4 Changes of cross-section

The changes in cross-section available on the

experimental unit take the form of continuous
expansion or contraction. For a continuous
change of cross-section, the coefficients of resis-
tance can be taken from special diagrams (section
7.3). For a discontinuous change in cross-section,
the coefficient of resistance can be derived from
A1 A2 Bernoulli’s equation and the principle of linear
momentum.
d1 d2
For expansion
2 2
æA ö æd 2 ö
z = çç 2 - 1÷÷ = çç 2 2 - 1÷÷ .
A1
A0 A2 è A1 ø èd1 ø

d1 d0 Accordingly, for contraction

2 2
æA ö æd 2 ö
Contraction of flow cross-section z = çç 2 - 1÷÷ = çç 2 2 - 1÷÷ .
è A0 ø èd 0 ø

Fig. 6.4 Change of cross-section Here, A0 and d0 respectively represent the con-
stricted cross-section. As this is normally un-
known, the coefficient of resistance for contraction
is taken from the following diagram.

0.6

0.4

z
0.2

0.0
0 0.2 0.4 0.6 0.8 1.0
Area ratio A2/A1

Fig. 6.5 Coefficient of resistance for discontinuous

contraction

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6.3.5 Experimental method

Connect two tube manometer or differential pres-

sure sensor (P2/1) to continuous expansion of
cross-section measuring glands (pipe section 6)
and perform measurement as described in section
5.3. Note the displays on the two tube manometer
and rotameter. Ensure that the signs are correctly
measured.
All Rights Reserved G.U.N.T. Gerätebau GmbH, Barsbüttel, Germany 05/2016

Repeat the measurement with continuous con-

traction of cross-section (pipe section 5).

Measured results
Pipe section 6: Expansion of cross-section 20 - 32,
continuous, d1=17 mm, d2=28.6 mm, l=145 mm

Volumetric flow V& Head loss hvges

in m3/h in mm

0.7 0
0.9 0
10.8 0
1.2 0
1.8 -15

Measured results
Pipe section 5: Contraction of cross-section 20 - 16,
continuous, d1=17 mm, d2=14.6 mm, l=145 mm

Volumetric flow V& Head loss hvges

in m3/h in mm

0.7 +200
0.9 +300
10.8 +415
1.2 +545
1.3 +570

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It is interesting that for expansion there is no pres-

sure loss; in fact a pressure gain occurs. The pres-
sure increase caused by the loss of speed out-
weighs the pressure drop caused by pipe friction,
at volume stream of 30 l/min.

6.4 Coefficient of resistance for pipe fittings

The experimental unit has a pipe section, in which

various fittings can be installed. In this section, the
coefficient of resistance for
– Ball cock
– Slanted seat valve
– Membrane valve
– Dirt trap
– Non-return valve
is determined by measuring the pressure drop.
When open, the ball cock has a totally smooth and
free passage cross-section.
Fig. 6.8 Ball cock
It can therefore be expected to have the lowest
pressure losses. Coefficients of resistance falling
as low as z R = 0. 03 can be reached.
Due to its jagged passage cross-section, the
slanted seat valve has a significantly higher coeffi-
cient of resistance in the range of z R = 1. 5 - 2. 0.
However, it is still significantly more favourable in
Fig. 6.6 Slanted seat valve terms of the flow than a standard DIN screw-down
stop globe valve, in which the flow has to be
diverted twice by 90°. Here, a coefficient of resis-
tance of around z R = 3. 0 can be expected.
For the membrane valve even high coefficients of
resistance (z R = 5 - 8. 5) can be expected.
The resistance value for the dirt trap depends on
Fig. 6.7 Membrane valve the filter insert. The smaller the passage

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cross-section of the holes, the greater the coeffi-

cient of resistance.
Non-return valves are given coefficients of
resistance of z R = 3. 5 - 5. 0 in the literature.

6.4.1 Experimental method

Connect two tube manometer or differential pres-

All Rights Reserved G.U.N.T. Gerätebau GmbH, Barsbüttel, Germany 05/2016

sure sensor to the measuring glands for the rele-

vant fitting (pipe section 7) and perform
measurement as described in section 5.3. Note
displays on two tube manometer or sensors and
rotameter in a table.

Volumetric flow V& Differential pressure Dp vges Head loss hvges

Fitting
in m3/h in mbar in mm

Ball cock 0.4 0.8 8

Membrane valve 0.4 9 88
Slanted seat valve 0.4 2.8 27
Dirt trap 0.4 50 491
Non-return valve 0.4 5 49

As expected, the ball cock demonstrates a

particularly low flow resistance.
The slanted seat valve is not as good as the ball
cock but has significantly lower resistance than the
membrane valve.

Due to the unfavourable sharp reversal of the

direction of flow, the membrane valve demon-
strates a particularly high resistance.

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However, even higher resistance can be observed

on the dirt trap. Nevertheless, this depends greatly
on the mesh size of the filter and the level of con-
tamination.

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6.4.2 Calculation of coefficients of resistance

The coefficients of resistance for the fittings are

now calculated using the following formula

2 hvges g l
zR = 2
-l .
v d

The distance between the measuring connections

is used as the length l.
All Rights Reserved G.U.N.T. Gerätebau GmbH, Barsbüttel, Germany 05/2016

Calculation of coefficients of resistancez for fittings

Internal diameter

Volumetric flow

number Re
Flow speed

Reynolds’
v in m/s
Length l
in mm

in mm

V& in
d

Fitting d/k
V& in m3/s
m3/h

Ball cock 17 160 0,4 11.6 × 10-5 0.51 7066 17000

Membrane valve 17 160 0,4 11.6 × 10-5 0.51 7066 17000
Slanted seat valve 17 160 0,4 11.6 × 10-5 0.51 7066 17000
Dirt trap 17 160 0,4 11.6 × 10-5 0.51 7066 17000
Non-return valve 17 160 0,4 11.6 × 10-5 0.51 7066 17000

Measured Coefficient of
l calculation ac- Coefficient of pipe
Fitting head loss hvges
cording to friction l resistance z
in m
Ball cock Blasius 0.035 0.008 0.27
Membrane valve Blasius 0.035 0.088 6.31
Slanted seat valve Blasius 0.035 0.027 1.71
Dirt trap Blasius 0.035 0.491 36.71
Non-return valve Blasius 0.035 0.049 3.37

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The coefficients of resistance given above could

be confirmed in the experiment. The coefficient of
resistance for the dirt trap depends on the filter in-
sert and the level of contamination.

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6.5 Opening characteristics of shut-off devices

In this experiment the restricting behaviour of the

shut-off devices is demonstrated using the
example of the membrane valve.
If shut-off devices are used to set particular
volumetric flows in pipe systems, at low opening
levels and volumetric flows, considerable attention
needs to be paid to good dosing capabilities.
All Rights Reserved G.U.N.T. Gerätebau GmbH, Barsbüttel, Germany 05/2016

Fig. 6.9 Shut-off device

The optimum is a progressive characteristic curve
where the opening level rises slowly at first then in-
creasingly quickly. Adjustment of the shut-off
device by a particular absolute amount results in a
corresponding percentage change in the volume-
tric flow.

Degressive
100% (shut-off valve)
Flow rate

Linear
50%

Progressive
(control valve)

0%
0% 50% 100 %
Opening
Fig. 6.10 Opening characteristics of valves

For example:
If a valve with a maximum opening of 10 revolu-
tions is opened from 1 to 2 revolutions, i.e. by 10%
absolute, and the volumetric flow will show a rela-
tive increase of e.g. 30%, e.g. from 1 to 1.3 l/min.

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This so-called “equal percentage” characteristic

curve is designated as progressive in the adjacent
diagram.

Plotted next to it are a linear and a degressive charac-

teristic curve, as occur on typical shut-off devices.

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6.5.1 Experimental method

The membrane valve is screwed into pipe section 7

and closed as far as it will go.

Open the valve by 1/4 revolution at a time and note

the volumetric flow.
Measured results:
All Rights Reserved G.U.N.T. Gerätebau GmbH, Barsbüttel, Germany 05/2016

Volumetric flow V&

Revolutions
in m3/h
0 0
1/4 0
1/2 0.524
3/4 0.752
1 0.953
1-1/4 1.039
1-1/2 1.090
1-3/4 1.102
2 1.113
2-1/4 1.132
2-1/2 1.133
2-3/4 1.170
3 1.181

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6.5.2 Evaluation of the experiment

The measured values recorded can be plotted

graphically against the opening of the membrane
valve.

1,20
Flow rate in m3/h

1,00

0,80

0,60

0,40

0,20

0,00
0,00 1,00 2,00 3,00
Opening

Fig. 6.11 Opening characteristics of valves

The valve opens quickly and is thus a typical

shut-off device. The membrane valve is equally
unsuitable for restricting a volumetric flow as the
slanted seat valve. By contrast, the ball cock is
much better suited as a shut-off device. However,
none of the shut-off devices included with the
experimental unit have a purely progressive
characteristic curve or the associated good
restricting properties.

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6.6 Pitot tube

The Pitot tube measures both the static (1) and the
total pressure (2). The difference between these
2: pges two values gives the dynamic pressure pdyn.

pdyn = p ges - p stat

The dynamic pressure is proportional to the

square of the flow speed and can be calculated as
All Rights Reserved G.U.N.T. Gerätebau GmbH, Barsbüttel, Germany 05/2016

1: pstat follows:
Fig. 6.12 Pitot tube
r. 2
pdyn = v
2

r: Specific density of water

The flow speed v can be determined from the
volumetric flow V& and the flow cross-section A.
V&
v =
A
The pressure difference can thus be used to
determine the volumetric flow for a given flow
cross-section.

6.6.1 Experimental method

The Pitot tube measuring object is screwed into

pipe section 7. The measuring glands are
connected to the two tube manometer or the differ-
ential pressure sensor. It must be ensured that the
static pressure is always lower than the total pres-
sure. The measurements are performed in accor-
dance with the instructions in section 5.3. The vol-
umetric flow is restricted with the slanted seat
valve in the test section inlet.

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This results in the following measured values:

Volumetric flow V& Dynamic pressure p dyn Dynamic height h dyn

in m3/h in mbar in mm

1.36 21.5 211

1.30 19.0 186
1.09 12.6 124
0.92 9.2 90
0.76 6.6 65

The temperature of the water is at 20°C, which

gives a specific density of water of

kg
r = 998.2 .
m3

6.6.2 Comparison with calculation

The free through-streamed pipe circular

cross-section A, is the difference of cross-section
of the pass through tube d1 and the cross-section
of pipe for total pressure measurement at Pitot
tube d2.

(d 12 - d 22 ) × p
A=
4

For steady turbulent flow in pipes of circular

cross-section the average speed v is described by
the ratio of the average flow speed v to the maxi-
mum flow speed vmax in consideration of the cor-
rection factor 0.84.

v
» 0.84
v max

This yields a average flow speed v.

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v » v max × 0.84.

This yields a calculated flow speed

V&calculated = A × v .

r p dyn
V& measured in m3/h V& calculated in m3/h
All Rights Reserved G.U.N.T. Gerätebau GmbH, Barsbüttel, Germany 05/2016

in kg/m3 in mbar
998.2 21.5 1.36 1.38
998.2 19.0 1.30 1.30
998.2 12.6 1.09 1.06
998.2 9.2 0.92 0.90
998.2 6.6 0.76 0.77

The consistency can be described as good.

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6.7 Volumetric flow measurement with nozzle/orifice

The volumetric flow cannot be determined from the

dynamic pressure alone. In technical fluid
mechanics, orifices or nozzles are frequently used
p1 p2 to determine the volumetric flow. Using a constant,
the volumetric flow to DIN 1952 and EN ISO 5167
can be calculated as follows:

2 × Dp
v& = a × e × Ad
r

Fig. 6.13 Nozzle/orifice – a: Flow coefficient

– e: Expansion coefficient
– Ad: Orifice cross-section
– Dp: Differential pressure (p1 - p2)
– r: Specific density
The flow and expansion coefficients for diameters
in the range 50 to 500 or 1,000mm are taken from
DIN 1952 and EN ISO 5167.

6.7.1 Experimental method

Once either the orifice or nozzle has been fitted in

the measuring object, it is installed in pipe section 7.

Caution! Ensure correct direction of flow.

When connecting the hoses to the measuring
glands and to the manometers or differential pres-
sure sensor, it must be ensured that the signs are
correct. The measurements are performed in
accordance with section 5.3. The volumetric flow is
adjusted using the reducing valve at the inlet to the
pipe section.

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The following measured values are obtained:

Measuring object: Nozzle; Water temperature 20°C

Volumetric flow V& Differential pressure Dp

in m3/h in mbar

1.3 28
1.1 20
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0.9 13
0.7 9

Measuring object: Orifice plate; Water temperature 20°C

Volumetric flow V& Differential pressure Dp

in m3/h in mbar

1.3 15
1.2 12
1.1 10
0.9 6.5

6.7.2 Comparison with calculation

To calculate the volumetric flow, the relevant

aperture cross-section is first determined.

d2
Ad = p ×
4

To determine the flow coefficient for both

experiments, the aperture ratio m is required.

d2
m=
D2

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D: Pipe diameter before shut-off device (28.5mm)

Ad=154 mm2 The following figures are calculated as the

aperture ratio for the orifice and the nozzle:
mNozzle = 0.24 mOrifice = 0.42
d = 14 mm
This results in flow coefficients in line with
DIN 1952: a = f (Re, m)The following f low
Fig. 6.15 Nozzle cross-section
coefficients can be used for the calculation:
a Nozzle = 100
. a Orifice = 0.67

Ad=268 mm2 As water is an incompressible medium, the

following applies for the expansion coefficients:
e Nozzle = e Orifice = 1

d = 18.5 mm

Fig. 6.14 Orifice cross-section

A comparison of the calculated and measured

volumetric flows then gives the following results.

Measuring object: Nozzle

V& measured in V& in m3/h

r in kg/m3 a e Dp in mbar m3/h
calculated

998.2 1 1 28 1.3 1.31

998.2 1 1 20 1.1 1.11
998.2 1 1 13 0.9 0.89
998.2 1 1 9 0.7 0.74

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Measuring object: Orifice plate

V& measured V& in m3h

r in kg/m3 Dp in mbar Variance in
a e in m3h/
calculated %

998.2 0.67 1 15 1.3 1.12 -14

998.2 0.67 1 12 1.2 1.01 -16
998.2 0.67 1 10 1.1 0.92 -16
998.2 0.67 1 6.5 0.9 0.74 -18
All Rights Reserved G.U.N.T. Gerätebau GmbH, Barsbüttel, Germany 05/2016

While volumetric flow measurement with the

nozzle shows an excellent result, an error of -14%
or more occurs in the calculation using the orifice
measurement. The difference between the
calculation and the measurement is caused by the
flow coefficient. The values taken from DIN 1952
are only applicable at diameters of 50 to 1000 mm.
As the flow cross-section here is smaller (d=18.5
mm), a must be corrected to approx. 0.8 to obtain a
meaningful comparison with the measured values.

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6.8 Venturi nozzle

Using the Venturi tube the law on the con-

servation of energy in fluid mechanics can be
demonstrated. The change of cross-section is
always associated with a change of speed. Apart
from a slight loss due to friction, the total
pressure remains constant. Bernoulli’s equation
Fig. 6.16 Venturi nozzle
with no loss element is

r v 12 r v 22
+ p1 + r g z 1 = + p2 + r g z 2
2 2

Assuming that the heights z1 and z2 are equal,

this gives

v 12 × r v 22 × r
p1 + = p2 +
2 2

After rearrangement this yields

r
p1 - p 2 = (v 22 - v 12 ) ×
2

The flow speed v can be calculated from the

volumetric flow V& and the flow cross-section A:

V&
v =
A

6.8.1 Experimental method

For measurements on the Venturi nozzle, either

the six tube manometer or connections P3 to P8 on
the pressure measuring unit are required. The
measuring glands are connected to the measuring
equipment using hoses. The measurements are
performed in accordance with section 5.3. The fol-
lowing sketch shows the flow cross-sections at the
measuring points.

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A1 A2 A3 A4 A5 A6
338.6mm² 233.5mm² 84.6 mm² 170.2 mm² 255.2mm² 338.6mm²

P3 P4 P5 P6 P7 P8
All Rights Reserved G.U.N.T. Gerätebau GmbH, Barsbüttel, Germany 05/2016

Fig. 6.17 Venturi nozzle with rectangular tube section

A higher pressure will occur at the point of the

greatest cross-section.
With a volumetric flow adjusted to V& von 0.5 m3/h ,
the following differential pressures are obtained:

Differential Height difference

Measuring point pressure
in mbar in mm
P3 - P4 +0 0
P4 - P5 +11 108
P5 - P6 -7 -69
P6 - P7 -2 -20
P7 - P8 -1 -10

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6.8.2 Comparison with calculation

The following energy changes can then be

determined between the measuring points.

Pressure difference: Pressure difference:

Measuring point Quadratic change of
speed v n2 + 1 - v n2 p n - p n +1 in mbar p n - p n +1 in mbar
n _ n+1
(measured) (calculated)
3_4 0.59²- 0.41² +0 +0.9
4_5 1.64² - 0.59² +11 +11.7
5_6 0.82² - 1.64² -7 -10.1
6_7 0.54² - 0.82² -2 -1.9
7_8 0.41² - 0.54² -1 -0.6

The relatively low variances between the

calculation and the measurement are caused by
friction losses.

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7 Appendix

7.1 Technical data

Overall dimensions of experimental unit

Length 2220 mm
Width 820 mm
Height 1980 mm
Weight approx. 250 kg
All Rights Reserved G.U.N.T. Gerätebau GmbH, Barsbüttel, Germany 05/2016

Electrical supply 230 V, 50 Hz

Nominal consumption (power) 0.75 kW
Optional alternatives, see rating plate
Pump
Centrifugal pump
Max. Head 24 m
Max. Capacity 7 m3/h
Water tank, capacity 75 L
Flow rate measurement
Rotameter
Measuring range 0.4 - 2.5 m³/h
Output 0 - 10 kW

Pressure measurement
Two tube manometer
Excess and differential pressure measurement
Filling medium Water
Measuring range 680 mm
(water column)
Six tube manometer panel
Excess and differential pressure measurement
Filling medium Water
Measuring range 390 mm
(water column)

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Differential pressure transducer

Measuring range 0 ... 200 mbar
Output 0 ... 10 V
Excess pressure sensor
Measuring range 0 ... 600 mbar
Max. pressure 1.2 bar
Output 0 ... 10 V
Thermometer
Range 0...60 °C

Pipe sections
– Straight pipe section, 1/2", St, galvanized, 1000 mm long
– Straight pipe section, 18 x 1, Cu, 1000 mm long
– Straight pipe section, 20 x 1.5, PVC, 1000 mm long
– Continuously constricted pipe section, 20 x 1.5 to 16 x 1.2, PVC
– Continuously expanded pipe section, 20 x 1.5 to 32 x 1.8, PVC
– Measuring section for installation of various measuring objects
– Pipe section with 90° angle and 90° bend, 20 x 1.5, PVC

Measuring objects
- Slanted seat valve d = 20 mm
- Membrane valve d = 20 mm
- Ball cock d = 20 mm
- Non-return valve d = 20 mm
- Dirt trap d = 20 mm
- with 4 different filter inserts
Pressure measurement tube (Pitot tube) Ø 17 mm
Pitot tube Ø 3 mm
Measuring orifice Ø 18.5 mm
Measuring nozzle Ø 14 mm
Venturi nozzle Ø 28.4 - 14.0 mm

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7.2 Bibliography

Wolfgang Kalide,
"Einführung in die technische Strömungslehre"
(Introduction to Technical Fluid Mechanics),
Carl Hanser Verlag,
6th revised edition, Munich, Vienna 1984

7.3 Tables and Diagrams

All Rights Reserved G.U.N.T. Gerätebau GmbH, Barsbüttel, Germany 05/2016

Kinematic viscosity of water as a function of

temperature (based on Kalide: Technische
Strömungslehre [Technical Fluid Mechanics])
Temperature in °C Kin. viscosity n in 10-6 m2/s
10 1.297
11 1.261
12 1.227
13 1.194
14 1.163
15 1.134
16 1.106
17 1.079
18 1.055
19 1.028
20 1.004
21 0.980
22 0.957
23 0.935
24 0.914
25 0.894
26 0.875
27 0.856
28 0.837
29 0.812
30 0.801

Tab. 7.1

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Wall roughness

Wall roughness of experimental pipes

Material Surface Wall roughness k
Copper pipe, Cu Technically smooth 0.001 mm
PVC pipe Technically smooth 0.001 mm
Steel pipe, St galvanized 0.1 mm

Diagrams
Instable

limit curve

sm
oot
hp
ipe
laminar turbulent (k=
0)

Fig. 7.1 Pipe friction coefficient corresponding to Colebrook and Nikuradse

(taken from "Dubbel: Taschenbuch für den Maschinenbau") [Engineering Handbook]

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Bend

Kneepiece
All Rights Reserved G.U.N.T. Gerätebau GmbH, Barsbüttel, Germany 05/2016

Fig. 7.2 Coefficients of resistance of smooth 90° elbows (from VDI Wärmeatlas 10. Aufl. 2006)

0.6
Coefficient of resistance z

0.4

0.2

0.0
0 0.2 0.4 0.6 0.8 1.0
Area ratio A2/A1

Fig. 7.3 Coefficient of resistance z for discontinuous

contraction

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Coefficient of resistance a
Diameter ratio d1/d2

Fig. 7.4 Wall friction factor for continuous contraction(nozzle)

as a function of contraction angle d
l1 + l 2
z=a
2
(from Kalide: "Einführung in die technische Strömungslehre")
Coefficient of resistance z

Diameter ratio d2/d1

Fig. 7.5 Coefficients of resistance for continuous expansion

(diffusor) as a function of contraction angle d

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7.4 Formulae

Pipe friction

Measurement performed by: Date:

Volumetric flow V& Head loss hv in mm

Differential pressure
Pipe section, type
in l/min p v in mbar
All Rights Reserved G.U.N.T. Gerätebau GmbH, Barsbüttel, Germany 05/2016

Calculation of head loss

Internal Volumetric flow Flow Reynolds’
Pipe sec- smooth /
diameter d speed in number d/k
tion
in mm V& in m3/h V& in m3/s m/s Re
rough

Calculated Measured
l calculation Coefficient of
Pipe section head loss hv head loss hv in Variance
according to pipe friction l
in m m

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Coefficients of resistance

Measurement
Performed by: Date:

Volumetric flow V& Head loss hvges in mm Differential pressure

Fitting
in l/min Dp vges in mbar

Calculation of coefficients of resistancez for fittings

Internal diameter

Volumetric flow
Length l in mm

Flow speed v

number Re
Reynolds’
d in mm

Fitting in m/s d/k

V& in m3/h V& in m3/s

Measured Coefficient of
l calculation Coefficient of Coefficient of
Fitting head loss hvges
according to pipe friction l resistance z resistance z90°
in m

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Flow rate measurement

Measurement
Performed by: Date:
Measuring object:
Water temperature:

Volumetric flow V& in m3/h Differential pressure Dp in mbar

All Rights Reserved G.U.N.T. Gerätebau GmbH, Barsbüttel, Germany 05/2016

Evaluation

Density r Flow Expansion Dp in mbar V& in m3/h V& in m3/h Variance

in kg/m3 coefficient a coefficient e measured calculated in %

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7.5 Index

!
6 tube manometer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
A
Absolute pressure calculation . . . . . . . . . . . . . . . . . . . . . 24
Annular chamber . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
Aperture ratio . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57 - 58
Atmospheric air pressure. . . . . . . . . . . . . . . . . . . . . . . . . 24
B
Ball cock . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
Bernoulli equation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
Bernoulli’s equation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60
Blasius . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
Bleed valve . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
Bleeding. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
C
Change in cross-section . . . . . . . . . . . . . . . . . . . . . . 37, 42
Coefficient of resistance . . . . . . . . . . . . . . . . . . . . . . . . . 37
Colebrook . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
Constriction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
D
DIN 1952 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56
Data acquisition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
Degressive characteristic curve . . . . . . . . . . . . . . . . . . . . 52
Differential pressure measurement . . . . . . . . . . . . . . 23, 27
Digital display. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
Dirt trap . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
Drain valve. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
Dynamic pressure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
E
Energy conservation law . . . . . . . . . . . . . . . . . . . . . . . . . 60
Excess pressure measurement . . . . . . . . . . . . . . . . . . . . 24
Expansion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
Expansion coefficient. . . . . . . . . . . . . . . . . . . . . . . . . 56, 58
F
Flow coefficient . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56, 58
Flow rate measurement . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
Flow speed . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
H
Head loss . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
K
Kinematic viscosity . . . . . . . . . . . . . . . . . . . . . . . . . . 35, 41

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L
Laboratory trolley . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
Leak test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
M
Measuring objects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
Measuring range . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
Membrane valve . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44, 49
Multifunction circuit board . . . . . . . . . . . . . . . . . . . . . . . . . 3
N
Non-return valve . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
All Rights Reserved G.U.N.T. Gerätebau GmbH, Barsbüttel, Germany 05/2016

Nozzle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56
O
Opening characteristic . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
Orifice . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56
P
Pipe angle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
Pipe bend . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
Pipe elbow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
Pipe fittings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
Pipe friction coefficient. . . . . . . . . . . . . . . . . . . . . . . . . . . 32
Pipe roughness . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
Pipe sections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
Pitot tube . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
Pressure loss . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
Pressure sensor. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
Pump . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
Q
Quick action coupling. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
R
Reynolds’ number . . . . . . . . . . . . . . . . . . . . . . . . . . . 31, 33
S
Scale . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
Shut-off device. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
Slanted seat valve . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
Specific density . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54, 56
Speed change . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
Switch cabinet . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
T
Total pressure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
Total pressure loss . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
Turbulent pipe flow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
Two tube manometer. . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

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V
Venturi nozzle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60
Visualisation program . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
Voltage signal . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
Volumetric flow measurement . . . . . . . . . . . . . . . . . . 53, 56
W
Work safety . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
Z
Zero point . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26

74 7 Appendix