HO CHI MINH NATIONAL UNIVERSITY

HO CHI MINH UNIVERSITY OF TECHNOLOGY

EXPERIMENTAL REPORT
FLUID MECHANICS

Instructor: Ph.D Tran Thanh Long

Class: CC01
Group: 04

STUDENT ID NAME
2353186 `Nguyen Trung Tin

Ho Chi Minh City, 6 November, 2024

 Group 4 – Fluid Mechanics Laboratory

EXPERIMENT 3A: ENERGY EQUATION

I. Fundamental theory
a. Objectives
Investigating the energy equation and calculate related parameters in flow when changing the
area of cross sections.

Figure 2.1

b. Theory
The energy of a unit weight of fluid at a section is determined by 3 components:
 Potential energy: zi
 Flow energy (pressure head): pi/g
 Kinetic energy (velocity head):
In which:
 zi; pi, Vi are height, pressure and velocity at section i-i, respectively.

 is kinetic energy correction factor. The occurrence of is due to the

inhomogeneous distribution of velocity in the flow section, given by formula:

(3.1)
In which:
 V: average velocity
 u: point velocity

To simplify calculation, for turbulent flows

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 Group 4 – Fluid Mechanics Laboratory

The energy equation from section 1-1 to section 2-2:

(3.2)
In which:
: The head loss due to friction from section 1 to section 2

Neglecting total head loss, the energy equation becomes:

(3.3)
From the equation above (3.3), if neglecting total head loss, the total head of the considered
interval is a constant and there is transformation of energy between potential energy and
kinetic energy.

II. Equipment:

Figure 2.2
The experimental equipment (see Figure 2.2) consists of the following components:
 Water is pumped from the reservoir (6) to the holding tank (1), flowing into the glass
channel via valve (2), which adjusts the flow rate.

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 Group 4 – Fluid Mechanics Laboratory

 The glass channel (3) is a rectangular, horizontal channel with a bottom width of B = 78
mm.
 A broad crested weir (4) with a trapezoidal cross-section, where the sides are inclined at
a 45° angle and the step height is a = 33.1 mm.
 The water level downstream of the step is adjusted using valve (5) located at the end of
the channel. The water then flows back into the reservoir (6) through a rectangular weir.
 A coordinate measuring probe (7) is mounted on the glass channel (3) to measure the
elevation of the channel bed and the water level inside the channel.

.
Figure 2.3

III. Procedure
Determine the location of the sections on the glass channel corresponding to points 1 to 6 in
the order from the upstream to downstream levels as shown in Figure 3.4. The distance
between sections is as follows:

L1-2 = L2-3 = L4-5 = L5-6 = 20cm; L3-4 =3.7cm

Determine bottom of the channel from 1 to 6 by point gauge and vernier. Write down the
results in Table 1 (in the report).
Use the valve ⑤ to adjust the flow and water level in the channel so that the downstream
water level is higher than the water level on the broad crested weir.

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 Group 4 – Fluid Mechanics Laboratory

Figure 3.4
The flow in the channel is stabilized, using point gauge and vernier determine Zi of water level
from sections 1 to 6. Note down the results in Table 1 (in the report).
Keeping the discharge constant, adjust the water level at downstream by the valve ⑤ (this time
the downstream water level is lower than the water level on the broad crested weir). Wait for
the water level in the glass channel to be stable, repeat the procedure in step 4. Write down the
results in Table 1 (in the report).

IV. Calculating
1. Calculations of velocity:
The average velocity at section i:
Vi = Q/Ai (3.4)
In which: Q=0,48l/s
Ai is the area of the cross-section i: Ai = Bhi;
Channel width is B = 78mm;
Water level from the bottom of the channel: hi = |Zđi - Zi|; (see figure 3.3)
Notice:
 Check if the whole system is safe to operate
 Switch ON switchboard.
 Observe the water level in the glass channel to prevent the overflow of water.

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 Group 4 – Fluid Mechanics Laboratory

2. Calculations of velocity head:

The average velocity head at section i:

(3.5)
3. Investigate the energy loss:
The energy loss between sections i and sections j was determined by applying the Bernoulli
equation (3.1) for these sections:
2 2
Vi Vj
hfij = (zi + pi + 2g
) - (zj + pj + 2g
) = (zi + hVi) - (zj + hVj) (3.6)

In which zi and zj are the water level at i section and j section; . where α = 1
and average velocity head is given by (3.5).
Apply (3.6) to calculate the energy loss form section 1 to section 2 (hf1-2), from section 2 to
section 3 (hf2-3), from section 3 to section 4 (hf3-4), from section 4 to section 5 (hf4-5), from section
5 to section 6 (hf5-6). Calculate for cases of water level.
4. Draw water level lines in the channel:
From the measured values hi and the calculated values hvi, plot the energy variation along the
channel from cross-section 1 to cross-section 6 in two cases:
 Case 1: Ignore energy losses between cross-section 1 and cross-section 6 for the case
water level downstream is lower than the water level on the broad crested weir.
 Case 2: Include energy losses between cross-section 1 and cross-section 6 for the case
water level downstream is lower than the water level on the broad crested weir

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 DATE: 24/10/2024 NAME OF INSTRUCTOR: Tran Thanh Long

EXPERIMENT 3A REPORT: ENERGY EQUATION

I. PREPARATION:
(Students must complete this section before coming to the lab. Failure to do so will
result in the student not being allowed to participate in the experiment.)
1. How can the water level and the channel bed elevation be measured?
To measure the water level , we use a measuring needle (7) mounted on glass channel
(3). First, we find out water level elevation Zi , which is measured from the top of the
channel to the water surface. Then we find out Zđi, which is the channel depth of each
section. Lastly, we use | Zđi - Zi | to get the water level of each section.
2. How can the water level in the glass channel be adjusted? How many downstream water
levels are tested?
To adjust the water level, we use valve (5) at the end of channel. There are two water
level needed to be tested: The downstream higher than the water level on the broad
crested weir and the downstream lower than the water level on that broad crested weir.

3. How many types of energy losses are encountered in this experiment?

There is one types only in this experiment: the energy losses along the water by friction
force from cross-section 1 to cross-section 6.
 Group 4 – Fluid Mechanics Laboratory

II. MEASUREMENT DATA:

Measurement of the bottom of the glass channel Zđ, the water surface Zi in the glass
channel at the cross section corresponding to different water level, the results recorded in
Table 1.
Table 1 Measurement data

No Section 1 2 3 4 5 6

Bottom height Zđ, cm 6.26 6.26 9.40 9.39 6.27 6.28

1 13.32 13.14 12.37 11.59 11.77 11.91

Water level Zi, cm
2 13.25 13.07 12.27 11.95 10.50 11.08

Distance from section i to section

i+1, cm 0 20 18,2 3,6 18,2 20

Accrual distance from section 1 to

section i+1, cm 0 20 38,2 41,8 60 80

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 Group 4 – Fluid Mechanics Laboratory

III. CALCULATIONS AND RESULTS:

1. Calculate the velocity of the flow and the average velocity head at the cross-sections of
Equations (3.4), (3.5). Calculating for two measured cases. The results are recorded in Table 2.
The average velocity at section i:
Q
Vi = A (3.4)
i

where Q = 0,48 (l/s); Ai = Bhi with B = 78mm = 7.8cm and hi = |Zđi - Zi|
2
Vi
hVi = (3.5)
2g
2. For two measured cases, calculating the energy loss (hf1-2) between the cross sections 1 - 2,
hf2- 3 between the cross sections 2 - 3, hf3-4 between the cross sections 3-4, hf4-5 between the
cross sections 4 - 5, hf5-6 between the cross sections 5 - 6 according to the formula (3.6). The
results are recorded in Table 2
We have:
2 2
Vi Vj
hfi-j = (zi + pi + 2g
) - (zj + pj + 2g
) = (zi + hVi) - (zj + hVj)
This equation determines the energy loss from section i to section j. However, the symbols 𝑧i
and 𝑧j might lead to confusion, as they can be interpreted as the water elevation. Therefore, I
have chosen to use ℎi and ℎj instead, which represent the water level measured from the
channel bottom to the water surface.

hfi-j = (hi + hVi) - (hj + hVj)

So, we need to calculate hi for convenience:

h1(cm) h2(cm) h3(cm) h4(cm) h5(cm) h6(cm)

1 7.06 6.88 2.97 2.2 5.5 5.63
2 6.99 6.81 2.87 2.56 4.23 4.8

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 Group 4 – Fluid Mechanics Laboratory

Table 2 The results of calculated velocity and energy losses

Energy losses hf5 -6, cm - 0.1271 - 0.5459

Energy losses hf4 - 5, cm - 2.9647 - 1.4832

Energy losses hf3–4, cm 0.5898 0.2498

Energy losses hf2 -3, cm 3.7318 3.7471

Energy losses hfl -2, cm 0.1780 0.1778

Sec 6 0.0610 0.0839

Sec 5 0.0639 0.1080

Average Sec 4 0.3992 0.2948

Velocity Sec 3 0.2190 0.2346
head hvi,
cm Sec 2 0.0408 0.0417

Sec 1 0.0388 0.0395

Sec 6 10.9305 12.8205

Sec 5 11.1888 14.5481

Average Sec 4 27.9720 24.0385
Velocity
Vi, cm/s Sec 3 20.7200 21.4420

Sec 2 8.9445 9.0365

Sec 1 8.7165 8.8038

No 1 2

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3. In figure 1, draw the bottom of the channel:
a) Based on the results in table 1, drawing on Figure 1 a "measuring waterline" (drawing for
the first water level).
b) Based on the results in table 1, drawing on Figure 1 a " ideal " waterline (drawing for the
first water level).
c) Discussing two "measuring" waterlines and "ideal" waterlines?

𝑖 = (2, 3, 4, 5, 6). So, we can apply this term to this energy equation:
The “ideal” waterline is obtained by removing the energy loss from section 1 to section

2 2
V1 Vi
z 1+ =z i+
2g 2g
Select the channel bottom as a datum (in this experiment, the bottom channel keeps
horizontal), then we can write:

𝑧i = ℎi, if section i is before or after the broad crested weir

𝑧i = ℎi + 𝑎, if the section i is on the broad crested weir
Q Q
Also Vi ¿ A ¿ B∗h , the energy equation becomes:
i i

 If section i is before or after the broad crested weir:

2 2
Q Q
h1 + 2 2
=hi + 2 2 (1)
2 g B h1 2 g B hi

 If section i is on the broad crested weir:

2 2
Q Q
h1 + 2 2
−a=hi + 2 2 (2)
2 g B h1 2 g B hi
Note that step (broad crested weir) height is a = 33.1 mm = 3.31 cm
We can use two equations (8) and (9) to find out the unknowns hi if the value on the left-hand
side is known, we can solve for hi from the cubic equation. Then, we can solve these equations
by using the trial and error method, or iteration method.

Water elevation ℎi (cm)

Table 3 The results of calculated water level

Section 1 2 3 4 5 6
Ideal 7.06
Measured 7.06 6.88 2.97 2.2 5.5 5.63
Accrual distance from
0 20 38.2 41.8 60 80
section 1 to i+1 (cm)
 Group 4 – Fluid Mechanics Laboratory

4. Discussing the water level between section 5 and section 6?

The difference in water level between section 5 and section 6 is 5.63 – 5.5 =
0.42 (𝑐𝑚), which is not too much
5.Please comment, compare, explain the energy loss of calculations power between the
sections in table 2.

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 EXPERIMENT 3D: MEASUREMENT OF VOLUMETRIC FLOW RATE
I. OBJECTIVES OF EXPERIMENT
Calculate air flow from pressure difference.
Comparison of flow measurement devices in a duct:
 Orifice plate.
 Venturi nozzle.

II. EQUIPMENT SET - UP

The fan inlet is a duct 149 mm diameter provided with pressure tapings whereby the
static pressure may be measured simultaneously at each of 4 sections. All four pressure tapings
are connected to a bank of pressurized manometer tubes (1,2,3,4). Two flow measurement
devices are:
 65mm orifice plat (1)
 149mm – 65mm diameter venturi nozzle (2).

Figure1: Experimental flowchart

In which:
1. Orifice plate
2. Venturi nozzle
3. Fans and electric motors
 Group 4 – Fluid Mechanics Laboratory

4. Inverter
5. Measuring tubes
6. Pressure gauges
7. Silicon tubes
1,2,3,4: Order number of the measuring tubes.

III. SUMMARY OF THEORY

The volume flow rate at the orifice plat and venturi nozzle in the pipe is determined by formula
as follows

(3.1)
Where:
Q: volumetric flow rate.
C: discharge coefficient.
Δp: pressure difference from inlet to throat. The manometer containing liquid of density ρ1 is
used to indicate Δp, the pressure difference may be expressed in terms of the manometric head
differential Δh by:
Δp = (ρ1 –ρ).g.Δh (3.2)
ρ : flow density ρ = 1.226 kg/m3 ρ1: water density ρ1 = 1000kg/m3
β : diameter ratio = d/D.
ε: expandability factor. The expandability factory is also detailed in the code and allows
for the effects of density change in gas flows where a high pressure reduction occurs. For liquid
flows and gas flows with moderate variation in pressure at the meter, ε = 1.00.
The discharge coefficients of the orifice plat and the venturi nozzle can be determined by
empirical formula. For the orifice
plate:

(3.3)
VD
Re= (3.4)
v

Where:

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 Group 4 – Fluid Mechanics Laboratory

Re: Reynolds number

U: upstream pipe velocity.
Q: discharge in pipe
D: diameter of pipe
μ: dynamic viscosity
When determining Q from Δp, it is necessary to estimate a value C initially as Re cannot be
calculated until Q is known. From an initial estimate of C (example C = 1), Q can be calculated
and thus Re found. The value of C can then be corrected and new values of Q and Re cure
calculated.
For the venturi nozzle:

(3.5)

IV. PROCEDURE
i. Check that there are no obstructions at the air intake and outlet of the gas pipe.
ii. Turn on the fan switch.
iii. Adjust the inverter speed to around 400 - 450 revolutions per minute (RPM).
iv. Read the water level in pressure tubes 1 and 2, and record the values in Table 1, in the first
row under the column "pressure tubes 1, 2." Read the pressure gauge on the left and record the
value in Table 1, in the first row under the column "pressure gauge."
v. Read the water level in pressure tubes 3 and 4, and record the values in Table 2, in the first
row under the column "pressure tubes 3, 4." Read the pressure gauge on the right and record
the value in Table 2, in the first row under the column "pressure gauge."

Repeat steps iii to v for three additional inverter speed values: 650-700 RPM, 900-950 RPM, and
1150-1200 RPM. Record the corresponding values in Tables 1 and 2.

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 DATE: 24/10/2024 NAME OF INSTRUCTOR: Tran Thanh Long

EXPERIMENT 3D REPORT: MEASUREMENT OF VOLUMETRIC FLOW RATE

I. PREPARATION:
(Students must complete this section before coming to the lab. Failure to do so will
result in the student not being allowed to participate in the experiment.)
1. What equipment is used to measure gas flow in the pipe for this experiment??
We use 2 quipments: the orifice plate and venturi nozzle.
2. How can the gas flow rate in the pipe be adjusted between measurements?
We can adjust the inverter speed to change the gas flow speed. So gas flow rate
changes, too.
Q = V.A
3. For a gas flow meter, how many measurements need to be taken, and what data should
be collected during each measurement??
We need 4 measurements to be taken: 400-450 RPM, 650-700 RPM, 900-950 RPM,
1150-1200 RPM. The data we should collect is room temperature before doing a
measurement. During each measurement, water height in 4 tubes, pressure gauge of
the left manometer (tube 1,2) for orifice plate, pressure gauge (tube 3,4) for venturi
nozzle will be taken.

II. MEASUREMENT DATA:

The air temperature: t0 = 29 oC ;
The air density: ρair = 1.1649 kg/m3
The air kinematic viscosity: νair = 1.6036x10-5 m2/s
The water density: ρwater = 995.7 kg/m3
 Group 4 – Fluid Mechanics Laboratory

III. MEASUREMENTS AND CALCULATES:

Table 1 Orifice plat

Difference
(Pressure
Frequenc tube Pressure gauge
y tube 2, h2 – h1 p1 – p2
gauge
Q
1, h1 - C
h2 (m) (m) (Pa) (m3/s)
(m) (Pa) measurin
g tube)
(%)

422 0.193 0.205 0.012 117.08 140 -16.38 0.567270 0.026971

677 0.182 0.214 0.032 312.19 330 -5.40 0.562076 0.043986

925 0.168 0.228 0.060 585.38 600 -2.44 0.561733 0.060193

1175 0.150 0.247 0.097 946.37 960 -1.43 0.561519 0.076505

Table 2 Venturi nozzle

Difference
(Pressure
Frequenc tube Pressure
y tube 4, h4 – h3 P3 – p4
gauge
gauge Q
3, h3 C
h4 (m) (m) (Pa) - (m3/s)
(m) (Pa)
measuring
tube) (%)

422 0.192 0.198 0.006 58.54 50 17.06 0.981112 0.033246

677 0.188 0.201 0.013 126.83 120 5.69 0.981112 0.048936

925 0.182 0.208 0.026 253.67 270 -6.05 0.981112 0.069207

1175 0.174 0.215 0.041 400.01 420 -4.76 0.981112 0.086906

IV. REPORT
1. Determine the discharge coefficients, the volumetric flow rate in 4 experiments by using
venturi nozzle and venturi nozzle (table 1, 2)
2. Explain the difference from the results of U tubes and pressure gauge?

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3. Compare the flow rates measured using the thin-walled orifice and the nozzle. Explain the
results.?

4. Which method (thin-walled orifice or nozzle) provides more accurate results? Why?

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