Measurement 39 (2006) 674–679

www.elsevier.com/locate/measurement

A new production technique for rotameters and venturimeters

Vedat Tanyıldızı, Haydar Eren *

Department of Mechanical Engineering, University of Firat, 23279 Elazıg, Turkey

Received 22 October 2004; received in revised form 22 December 2005; accepted 22 December 2005
Available online 15 February 2006

Abstract

In this work, a simple and cheap production technique for the liquid and gas flow meters widely used in industry is
presented. The technique is concerned with the production of the flowmeter case and simply employs the relative equilib-
rium property of a liquid in a container rotating with constant angular velocity. The liquid used is a special chemical solid-
ifying during the process. Naturally, a tube with a paraboloidal inner surface is obtained and this tube can be used as the
flowmeter case. A comparison of the flow rate computations shows that flowmeters with paraboloidal inner surfaces thus
obtained provide, in fact, a slightly better approximation than the usual flowmeters with conical inner surfaces.
Ó 2006 Elsevier Ltd. All rights reserved.

Keywords: Rotameters; Venturimeters; Centrifugal casting technique

1. Introduction The equipment could be thought as an orifice

with variable area. Downwards resultant force,
The rotameter is a vertical glass tube containing a consisting the difference between gravitational force
float as shown in Fig. 1. The tube was slightly and buoyancy force, is constant. Due to this,
tapered in bore with the diameter decreasing down- upward force which is the product of pressure dif-
wards; and the fluid flow to be measured passed ference and projectional area of the float should
upwards through the conical tube, which was be constant to equalize with the downward force.
inserted in the flow circuit. The floats was carried Because of the cross-sectional area of the float is
upwards by the passage of the fluid until it reached constant, pressure difference through the float
a position in the tube where its weight was balanced should also be constant. If the flow area is kept
by the force due to the fluid flowing past it. The dis- constant, dp should change with square of the
placement of the float in the tube is a measure of the velocity. Uniquely, dp is kept constant by using
volume rate of flow and the tube may be calibrated downwardly tapering tube providing axially vari-
in volume flow units [1,2]. able flow area.
For each flow rate over the measurement inter-
val, the float stands on the different axial positions.
*
Corresponding author. Tel.: +90 424 237 00 00/3658; fax: +90
Namely, float’s each position corresponds different
424 241 55 26. flow rate of the fluid flow. By calibrating those posi-
E-mail address: haydar_eren@yahoo.com (H. Eren). tions, a scale is obtained.

0263-2241/$ - see front matter Ó 2006 Elsevier Ltd. All rights reserved.
doi:10.1016/j.measurement.2005.12.011
 V. Tanyıldızı, H. Eren / Measurement 39 (2006) 674–679 675

Nomenclature

Q volume flow rate (m3/s) g local gravity acceleration (m/s2)

Cd flow rate coefficient VF float volume (m3)
AT cross-sectional area of the rotameter ver- qF float density (kg/m3)
sus the place of the float (m2) q fluid density (kg/m3)
AF cross-sectional area of the float (m2)

Q ¼ K 1 þ K 2y ð4Þ

where K, K1, K2, are all constants [3].

The float used in rotameters can be constructed
from various substances in order to make difference
of density (qF  q). Thus the volume rate of flow
can be measured. To keep stable in the axis of rota-
meter of the floats which is not spherical is not easy.
For this purpose, curved channels are made on the
surface and thus float can be rotation around the
vertical axis.
Some common floats are indicated in Fig. 2.
Floats should be able to move easily inside of the
tube. In order to see the place of the float, rotame-
ters are generally made from durable glass. If a bet-
ter strength is required, the tube can be manufacture
from metal and the place of the float along the wall
is determined magnetically. If a pneumatic or elec-
Fig. 1. Variable area rotameter. trical signal relevant to flow rate are required, the
movement of the float is sensed by a suitable dis-
For incompressible flow placement transducer.
rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Glass tube rotameters may be selected to measure
C d ðAT  AF Þ q q
Q ¼ qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2gV F F ð1Þ the flow rate of liquids ranging from very low flows
2 qAF of 30–300 ml/s up to flow rates as high as 0.5–5 l/s.
1  ½ðAT  AF Þ=AT 
If air is the metered fluid, however the equivalent
where Cd is flow rate coefficient. range of flow is from about 0.2–2.0 ml/s to about
If the flow rate coefficient, Cd, varies slightly 4–40 l/s. When liquids are metered the smaller
depending on the place of the float and always size glass tubes can only be used up to about
[(AT  AF)/AT]2  1, the latter equation can be 0.8 kN/m2. When gases are metered the upper limits
written as follows: are much lower [1,4,5].
rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
q q
Q ¼ C d ðAT  AF Þ 2gV F F ð2Þ
qAF
Since the terms within the square root are constants
it will be able to be arranged as below.
Q ¼ KðAT  AF Þ ð3Þ
If the contraction angle of the rotameter is
selected appropriately, the meter on it varies linearly
relatively to the y axis distance of the float. Finally it
will have a linear relationship as follows for volume
flow rate. Fig. 2. Rotameter floats.
676 V. Tanyıldızı, H. Eren / Measurement 39 (2006) 674–679

dense and voidless structure is obtained due to the

pressure gradient increases in normal direction to
the free surface of the liquid. Besides these advanta-
ges, this technique is superior since no sprue, gate or
riser and cooler are required during the process.
In the manufacturing of the tapered pipe of the
rotameter, to obtain direct casting by centrifugal
technique providing last finish condition on the sur-
face without machining, it is necessary to investigate
the relative balance statute of the material used.
Fig. 3. Venturi tube. A fluid inside a cylindrical tube which rotates
around a vertical axis in a constant angular velocity
On the other hand, the venturi tube consists of a will be reach to the angular velocity of the tube and
conical convergent entry leading to a cylindrical it will rotate together with the tube. In this situation
throat followed by a conical divergent outlet. The which is known as ‘‘forced vortex’’, the free surface
upstream pressure tapping is located at a distance of the liquid is a paraboloid obtained by axially
of one half of one pipe diameter upstream of the rotating the parabola of
convergent entry, while the downstream pressure x2 2
tapping is located in the throat. y¼ r ð6Þ
2g
Pressure tappings may be either single holes, or a
number of holes around the section communicating If it is reached to high speeds by closing the mouth of
with an angular chamber from which the pressure is tube, the overflow can be prevented and a discrete
tapped-off to the manometer; the BSI specify that paraboloid takes place along h0, glass height (Fig. 4).
the diameters of any pressure holes must not exceed Angular velocity and the rotation of the tube
0.1di on the upstream side and 0.1d1 at the throat depending on the values, h0, r1 and r2 as follows:
sffiffiffiffiffiffiffiffiffiffiffiffiffiffi
(Fig. 3).
2gh0
The conical angle for the inlet cone is normally x¼ ð7Þ
21° ± 2°. British Standard 1042 specifies two conical r22  r21
angles, 5–7° and 14–15° for the outlet cone. The 30x
n¼ ð8Þ
design of the outlet cone has a major influence on p
efficiency in terms of pressure loss.
Considering the streamline flow of an incom-
pressible fluid through the venturi tube; if the
velocities at the throat and the upstream of the con-
striction is respectively v1 and vi, the Bernoulli equa-
tion can be applied and it may be show that
sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
2gh
Q ¼ C d A1 ð5Þ
1  ðA1  Ai Þ2
where A1 is the area of minimum cross-section of
the venturi tube and h is the equivalent differential
pressure head (in meters of fluid being monitored).
The value of CD for a venturi will approach
unity, a typical value being 0.97.

2. Manufacturing technique

The horizontal, vertical or tangential centrifugal

casting in the manufacturing of hollow cylindrical
parts has a particular importance due to their sim-
plicity. During spinning process, homogenous, more Fig. 4. Relative equilibrium of rotating liquids.
 V. Tanyıldızı, H. Eren / Measurement 39 (2006) 674–679 677

If r0 is taken into consideration, the volume of the

fluid which should be put into tube to construct
the rotameter is obtained as follows:
V ¼ p½r20 h0  ðr22 y 2  r21 y 1 Þ=2 ð9Þ
While a rotameter is constructed to measure the
flow rate at specified ranges of a fluid, the followings
can be implemented respectively: Flow rate coeffi-
cient, Cd, is selected a value between 0.6 and 0.8 which
will be modified later. AT, AF, qF, VF values in the Eq.
(2) can be arranged to provide the least flow rate that
is required to measure. With the aim of obtaining
high sensitivity, a ratio between 5/1 and 10/1 is taken
for the measured maximum and minimum flow rate
and then, the maximum flow rate is found. The pro-
cedures could be performed by being selected the Fig. 5. Rotameter manufacturing.
maximum flow rate. In this way, by taking r1 in the
narrow portion and r2 in the wide portion of the
radius at the tapered tube; the outer diameter of the
rotameter is found as r0 if we consider the desired
thickness. The length of the centrifugal pot h0 is taken
the reasonable length to decrease the reading mis-
takes on the meter. The body length of the rotameter
is increased by considering the float length, the dead
zones of two ends where the measurement cannot
be performed and the joining distance; depending
on this increasing, r1 is decreased and r2 is increased.
x, the angular velocity of the centrifugal pot, is calcu-
lated from Eq. (7) in which is substituted the changed
and make the measurement possible values or r1, r2
and h0 and then, the rotation of the centrifugal pot
is calculated by using Eq. (8). y1 and y2 values versus
r1 and r2 are calculated by using Eq. (6). After that,
the value of the liquid material is found by using
the other known parameters and Eq. (9).
Venturimeter production is also in same manner.
The input cone and throat section corresponding to
down part is designed with sprue. The inner surface
of diffuser section, like paraboloid rotameter, will be
paraboloid during the rotation at an angular veloc-
ity such as x (Fig. 6). Here, flow rate coefficient is Fig. 6. Venturimeter manufacturing.
selected 0.90 to change later. Dimensions are then
specified depending on maximum flow rate to be solidify the liquid polyester, 20 ml/kg hardener
measured. At the end of the process, the liquid vol- recommended by the manufacturer and 50 ml/kg
ume to put into container is calculated as follows: catalyzer is added. After the centrifuge continuing

15–20 min, the rotameter having high quality inner
V ¼ p ½r20 h0  ðr22 y 2  r21 y 1 Þ=2 þ 2r31
surface can be obtained (Figs. 5 and 6).

h1 2 2 2
þ ðri þ ri r1 þ r1 Þ þ ri ð10Þ 3. Results
3

Flowmeters are molted from polyester substance From the view point of the measurement sensitiv-
which solidifies because of chemical reaction. To ity, the proposed rotameter manufactured by the
678 V. Tanyıldızı, H. Eren / Measurement 39 (2006) 674–679

centrifugal technique are seen much higher qualities. The flowmeter body was manufactured by using
The inner surface in the rotameters manufactured spinning equipment with adjustable revolution.
by the other techniques is the form of cut cone, as Prescribed amount of liquid polyester was filled into
seen in Fig. 1. In each position of the float, the flow a cylindrical mould and spinned around by
area between the surface and the float can be shown 1400 rev/min. A chemical reaction of solidification
as follows took place during spinning. Then, solid paraboloid
2 body of the flowmeter having the dimensions of
AT  AF ¼ ðp=4Þ½ðD þ ayÞ  d 2  ð11Þ
h0 = 390 mm, r1 = 22.5 mm and r2 = 29.5 mm was
where constant ‘a’ represents the obstruction of the formed. After settling the float and mounting the
cone depending on the axial distance. It is desired couplings to a vertical flow line over the unit in
that the meter mounted on the rotameter linearly our laboratory, calibration experiments with water
changes with the flow area. However, this is impos- were executed and the results were obtained as seen
sible because of a2y2 term in Eq. (11) except very in Fig. 7.
small ‘a’ values. This is an important limit for mea- A conventional flowmeter having the dimensions
surement sensitivity [3]. On the other hand, the flow of h0 = 300 mm, r1 = 22.5 mm and r2 = 25.5 mm
area of the presented rotameter with parabolic inner was also tested with water in the same manner
surface is written as and the results were obtained as seen in Fig. 8.
2 Although their measurement ranges are different
AT  AF ¼ ðp=4Þ½ð2rÞ  d 2  ð12Þ
due to the differences on the dimensions of floats
If Eq. (6) is used, then we have, and bodies, the calibration results are quite conve-
nient for the verification of the argument: Measure-
2pg pd 2
AT  AF ¼ y  ð13Þ ments with the paraboloidal flowmeter in whole range
x2 4 change linearly (Fig. 7). Contrarily, the calibration
As easily seen in Eq. (13), the flow area is a linear curve of conventional flowmeters is not linear as
function of the axial distance. For this reason, the seen in Fig. 8. To ensure correct measurements with
reliable measurement sensitivity is obtained without them it is necessary to keep the top angle of conical
any assuming and limit. However the obtained re- body in 5–7°. The paraboloidal flowmeter have no
sult does not mean that ratios of the tapered such a constraint. Eventually, simply application
cross-section can randomly be selected. of paraboloidal inner shape to flowmeter tube with
The main idea of the derivation of Eq. (1) is to
use Eq. (14), which the force-balance on the float.
F D þ q  gV F ¼ qF gV F ð14Þ 300
Float distance (mm)

250
Having different VF volumes and AF areas, floats 200
can be manufactured from different materials 150
depending on the drag force FD, the specific weight 100
of the fluid and the flow measurement space. As the 50
other types of rotameters, the rotameters manufac- 0
0 0.5 1 1.5 2 2.5
tured by the proposed technique must be calibrated
Mass flow rate (kg/s)
for measuring. The linear relation between the flow
rate and float easily gets the calibration of the man- Fig. 7. Calibration curve for a paraboloid rotameter.
ufactured paraboloid rotameter. After the calibra-
tion tests are performed for the minimum and
maximum limits at the measured flow rates, the 300
Float distance (mm)

space between the determined two axial positions 250

can equally be marked. This process positively 200
150
affects to measurement sensitivity.
100
Rotameter, manufactured to measure flow rates
50
of fluids, can be calibrated by measuring the flow 0
quantity per unit time intervals. If the fluid is gas, 0 0.1 0.2 0.3 0.4 0.5 0.6
Mass flow rate (kg/s)
an additional set-up is required for the calibration
[6,7]. Fig. 8. Calibration curve for a conventional rotameter.
 V. Tanyıldızı, H. Eren / Measurement 39 (2006) 674–679 679

a special production technique produces a new mea- reaction. The surface becomes roughness because
surement device. of the centrifugal casting. With the same mecha-
A reciprocal calibration of conical and paraboloi- nism, it is possible to manufacture devices which
dal flowmeters for the same measurement range does can measure for different flow rate intervals.
not give any benefit. Because, it is quite possible to The venturimeter manufactured by the proposed
fix the measurement range of a flowmeter up to a cer- method is a measurement device which can be easily
tain interval by changing input/output diameters of manufactured in small workshops and has low pres-
the body, float mass and float shape. Briefly, the only sure-drop. It is easy to mold and it is not required to
meaningful comparison between those different flow- give serious attention during casting.
meter types whether their calibration curves are linear It is clearly seen that this manufacturing tech-
or not. It is quite clear that the production of a flow- nique is very useful for the engineers and researchers
meter with dimensions assuring the desired range is who have to work in the difficulty of limited labora-
possible for any liquid or gas flow measurement. tory conditions.

4. Conclusion References

The manufacturing of rotameter by using vertical [1] C.V. Collett, A.D. Hope, Engineering Measurements, Long-
centrifugal casting technique is useful from the man Scientific and Technical, 1983.
[2] E. Ower, R.C. Pankhurst, The Measurement of Air Flow,
point of both economical and sensitive dimensional
Pergamon Press, 1977.
property: in the manufacturing of traditional rota- [3] E.O. Doebelin, Measurement Systems—Application and
meter with conical shape by using static casting, Design, McGraw-Hill, 1975.
moulding and machining, difficulty on sensitive [4] J.F. Douglas, Fluid Mechanics, Longman, 1987.
machinability and high costing price is considered. [5] J.P. Holman, Experimental Methods for Engineers, McGraw-
However, the manufacturing of rotameters having Hill, 1966.
[6] R.W. Miller, Flow Measurement Engineering Handbook,
parabolic interior surface is very easy with the sug- McGraw-Hill, 1983.
gested manufacturing technique in the case of using [7] A.T.J. Hayward, Flowmeters—A Basic Guide and Source
the chemical substances which solidify during the Book for Users, Macmillan, 1983.