About Reynolds number and venturimeter

1. UNIVERSITY FOR DEVELOPMENT
STUDIES
TAMALE, NYANKPALA CAMPUS
DEPARTMENT OF MECHANICAL AND INDUSTRIAL
ENGINEERING
MECHANICAL ENGINEERING LAB-Ⅰ
FLUID MECHANICS EXPERIMENTAL REPORT
INDEX NUMBER:
MEN/0064/20
NAME OF CO-ORDINATOR
Ing. Ebenezer Omari Abankwa
MAY 4 – MAY 6, 2022

2. ACKNOWLEDGEMENT
I would like to express my deepest appreciation to all those who provided me the possibility
to complete this Laboratory work and putting together as a single work piece. A special
gratitude I give to our able coordinator, Ing. Abankwa, whose contribution in stimulating and
encouragement helped me to come this far in writing this report.
Furthermore, I would also like to acknowledge with much appreciation the crucial role of the
Lab instructor, Mr. Shadrack Osei Boateng who invested his full effort in teaching and
guiding us throughout the experiments to achieve this goal. A special thanks also goes to all
the Teaching Assistants who in a special way guided us find solutions to some challenges we
encountered.
Finally, I would like to appreciate my group members for the unity exhibited during the
period of the laboratory

3. Contents
ACKNOWLEDGEMENT.............................................................................................................................2
EXECUTIVE SUMMARY............................................................................................................................4
SECTION A ..............................................................................................................................................6
REYNOLDS EXPERIMENT .....................................................................................................................6
Aim..................................................................................................................................................6
Theory .............................................................................................................................................6
Laboratory Procedure.....................................................................................................................6
Simulation Procedure ...................................................................................................................7
Observation & Results.....................................................................................................................7
Discussion......................................................................................... Error! Bookmark not defined.
Conclusion........................................................................................ Error! Bookmark not defined.
SECTION B ............................................................................................................................................10
VENTURIMETER.................................................................................................................................10
AIM................................................................................................................................................10
THEORY .........................................................................................................................................10
Procedure & Experiment...............................................................................................................14
Results and observations..............................................................................................................24
Discussion......................................................................................... Error! Bookmark not defined.
Conclusion.....................................................................................................................................25

4. EXECUTIVE SUMMARY
The mechanical engineering laboratory is an engineering course that exposes students to the
practical aspects of theories studied in the classroom.
All these experiments were conducted using Fluid mechanics virtual laboratory which is an
inbuilt software designed by some specialists to aid students appreciate the theories studied in
class better. The virtual lab is accessible to all students since some do not have access to the
physical laboratory.
Internet connection and the virtual laboratory website were the requirements for the
experiments.
The experiments were conducted severally to ensure accuracy.
The report is partitioned into two sections with the first section being the Reynolds
experiment. This experiment is to illustrate laminar, transitional and turbulent flows and also
determine the conditions under which these types of flow occur.
The second section is the Venturimeter experiment. The main objective of this experiment is
to determine the coefficient of discharge of a given ventrimeter, taking into consideration the
Reynolds number.
In conclusion, all the experiments were conducted to determine the types of flows and their
associated equations such as the Bernoulli equation and the Reynolds number. The
considered medium of flow is the pipe.
I hereby encourage all students and stakeholders to make use and patronize the virtual
laboratory system since it is easily accessible and can be used in institutions where the
physical laboratory equipment is absent.

5. INTRODUCTION
The mechanical engineering laboratory is an important component of the engineering
students of the University for Development Studies. It exposes students to the practical
aspects of theories studied in the classroom via virtual laboratory experiment. It covers
different topics in some engineering courses of which some of these courses are; strength of
materials and fluid mechanics. It also involves certain software such as MATLAB and
Arduino. The experiments consist of two sections;
The Reynolds experiment which is to determine the Reynolds number
The Ventrimeter experiment which is to determine the coefficient of discharge of a given
Venturimeter and to verify the Bernoulli’s equation.

6. SECTION A
REYNOLDS EXPERIMENT
Aim
To study different patterns (laminar, transition, and turbulent regimes) of a flow through a pipe
and correlate them with the Reynolds number of the flow.
Theory
For a particular fluid flow, depending on the velocity, the flow shows the laminar, transition
and turbulent patterns. In laminar flow, the fluid flows in a layer without disturbing the other
layer, whereas in turbulent flow the fluid does not follow any regular layer and the flow is
highly chaotic. The flow shows the randomness of turbulent flow due to elevated dissipation.
The flow exhibits intermittent behaviour in the transition regime, sometimes laminar and
sometimes turbulent. You can compare the essence of the flow with a non-dimensional number
called the Reynolds number.
Reynolds number is defined as the ratio of inertia to viscous force in a flow. For a particular
fluid i.e., for constant viscosity, the flow transits from laminar to turbulent as the velocity of
the flow is increased. The Reynolds number at which the flow starts to transit from laminar is
called the critical Reynolds number.
The Reynolds number for a flow in a pipe is obtained using following equation:
Re=(ρvd)/μ where, ρ is the density, V is the average flow velocity in the pipe, D is the pipe
diameter and μ is the dynamic viscosity.
The flow transits from laminar to turbulent for a specific fluid, i.e., for continuous viscosity, as
the flow velocity is increased. The critical number of Reynolds is the Reynolds number at
which the flow begins to transition from laminar to turbulent. The essential Reynolds number
for a flow through a pipe is generally calculated to be 2300. On the basis of the experimental
data, Reynolds classified the flow regimes as follows:
Laminar < 2300
2300 < Transition < 4000
Turbulent > 4000
Laboratory Procedure
1. Close the drainage valve of the constant head tank if it is in open position.
2. Switch ON the main power supply and then switch ON the pump.
3. Open the control valve of water supply to constant head tank and partially close the
bypass valve. Wait till overflow occurs.

7. 4. By partially opening the control valve provided at the end of the tube, the minimum
flow of water through the glass tube is regulated.
5. Change the flow of dye by the flow adjustment arrangement through the needle such
that a fine colored strand is observed.
6. Observer, note down the flow pattern observed (laminar, transition or turbulent).
7. Measure the flow rate using measuring cylinder, stop watch and calculate the Reynolds
number.
8. Repeat the above 2 steps for different flow rates by adjusting the control valve.
9. Switch OFF the pump and drain the apparatus completely once the experiment is over.
10.
Simulation Procedure
1. Click on the Power button to turn on.
2. Once powered up a slider will appear right to the valve.
3. Move the slider to regulate the flow of water through the glass tube.
4. The flow can be observed in the magnified view of the glass tube below the apparatus.
5. Press the save button to save the readings.
6. Take 10 readings.
7. To access the readings click show observation table.
8. You can export the observation table to an excel file by clicking on export to excel
button.
9. In case you need to repeat the experiment just refresh the page.
Observation & Results
R1 (ml) R2 (ml) Time (s)
5 144 10
6 229 12
7 298 12
8 561 14
9 484 14
10 404 15
12 162 12
13 312 13
14 457 15
16 487 12

8. 0
2
4
6
8
10
12
14
16
0 2 4 6 8 10 12 14 16 18
R1 vs Time

9. Observation
Observation I
When velocity of water flow is low, dye filament will be in the form of straight line in the glass tube.
It could be seen in the glass tube that dye filament is in the form of straight line and parallel to the
wall of glass tube. Above condition is the example of laminar fluid flow. Therefore, at lower velocity
of water flow through the glass tube, the type of water flow will be laminar.
0
2
4
6
8
10
12
14
16
0 100 200 300 400 500 600
Axis
Title
R2 vs Time

10. SECTION B
VENTURIMETER
AIM
To determine the coefficient of discharge of given venturi meter.
THEORY
Venturimeter is a flow measurement device, which is based on the principle of
Bernoulli's equation. Inside the pipe pressure difference is created by reducing the cross-
sectional area of the flow passage. This difference in pressure is measured with the help of
manometer and helps in determining rate of fluid flow or other discharge from the pipe line.
Venturimeter has a cylindrical entrance section, converging conical inlet, a cylindrical throat
and a diverging recovery cone.
Components of Venturimeter
a) Cylindrical entrance section: This is the section having the size of a pipe to which it is
attached. The venturimeter should be proceeded by a straight pipe of not less than 5 to 10
times the pipe diameter and free from fittings, misalignment and other source of large-scale
turbulence.
b) Converging conical section: The converging takes place at an angle of 21±2°. The
velocity of fluid increases as it passes through the converging section and correspondingly
the static pressure falls.

11. c) Throat: This is a cylindrical section of minimum area. The velocity is maximum and the
pressure is minimum. The throat diameter is usually between ½ to ¼ of the inlet diameter.
Length of the throat equals its diameter.
d) Diverging section: This is a section in which there is a change of stream area back to the
entrance area. The recovery of kinetic energy by its conversion to pressure energy is nearly
complete and so the overall pressure loss is small. To accomplish a maximum recovery of
kinetic energy the diffuser section is made with an included angle of 5° to 7°. This angle has
to be kept less so that the flowing fluid has least tendency to separate out from the boundary
of the section.
Types of Venturi Tubes
1. a standard long-form or classic venturi tube
2. a modified short form where the outlet cone is shortened
3. an eccentric form to handle mixed phases or to minimize build-up of heavy materials
4. a rectangular form used in duct work
The major disadvantages of this type of flow detection are the high initial costs for
installation and difficulty in installation and inspection. The Venturi effect is the reduction in
fluid pressure that results when a fluid flows through a constricted section of pipe. The fluid
velocity must increase through the constriction to satisfy the equation of continuity, while its
pressure must decrease due to conservation of energy: the gain in kinetic energy is balanced
by a drop in pressure or a pressure gradient force. An equation for the drop in pressure due to
venturi effect may be derived from a combination of Bernoulli’s principle and the equation of
continuity.
Let d1 = Diameter at inlet or at section 1,
V1 = velocity of fluid at section 1

12. P1 = Pressure at section 1
and d2, V2, a2 and P2 are the corresponding values at section 2.
Applying Bernoulli’s equations at section 1 and section 2, we get,
Since the pipe is horizontal, so z1 = z2
Now applying continuity equation at section 1 and 2
Substituting value of v1 in equation (1.4) we get

13. Where,
x = difference between the liquid column in U tube,
ρL = density of lighter liquid,
ρ = density of liquid flowing through pipe.
But, discharge through venturimeter,
Q=a2v2
Equation (1.5) gives the discharge under ideal conditions and is called as theoretical
discharge.

14. Actual discharge is given by,
Actual discharge = Coefficient of venturimeter x Theoretical discharge
Recovery of Pressure Drop in Orifices, Nozzles and Venturimeters:
The pressure drop in orifice meter and nozzles are significantly higher than the venture
meters. Venturi causes less overall pressure loss in a system and thus saves energy: the
overall pressure loss is generally between 5 and 20 per cent of the measured differential
pressure. The venturimeter has an advantage over the orifice plate in that it does not have a
sharp edge which can become rounded; however, the venturimeter is more susceptible to
errors due to burrs or deposits round the downstream (throat) tapping. The lengths of straight
pipe required for upstream and downstream of a venturimeter for accurate flow measurement
are given in ISO 5167-1: 1991.
Procedure & Experiment
1. Open Venturimeter experiment, a window will appear as shown.

15. 2. Select the required diameter of pipe, then click NEXT button.

16. 3. Click on the main inlet valve to allow the flow through it.

17. 4. Click on pipe inlet valve to allow the flow through it.

18. 5. Click on manometer knot to change it from isolated position to air-vent position to remove
air bubbles and again click to change it to read position.

19. 6. Here the manometer reading is noted down. The calculate the value of Head Loss.
Diameter= 50
Length =3m
LL =42
RL=29
Headloss=163.7999
D1=5cm
D2=2.72cm
Time=12sec
Qact=281.5cm3
/sec
Qth=3448.5cm3
/sec
Cd=0.82
Diameter= 40mm
Length =3m
LL =41.1
RL=25.9
Headloss=191.52cm
D1=4cm
D2=2.366cm
Time=13.3sec
Qact=2537.59cm3
/sec
Qth=2877.1643cm3
/sec
Cd=0.88

20. Diameter= 20mm
Length =3m
LL =42
RL=40
Headloss=25.2cm
D1=2cm
D2=1.36cm
Time=95sec
Qact=355.2632cm3
/sec
Qth=363.4944cm3
/sec
Cd=0.98

21. 7. Click on tank outlet valve to close it to measure the discharge.

22. 8. The observation and calculations of the trial is given here.

23. 9. Calculate actual discharge, theoretical discharge and coefficient of discharge. Repeat the
same procedure for other trials.

24. Results and Discussion
The experiment is conducted to measure the flow of water through a pipe by means of a
venturimeter which is connected to a manometer in order to measure the difference of height in the
manometer reading due to the change in pressure in the two limbs of the manometer. The same
experiment is repeated a number of times with different flow rate by regulating the inlet valve. by
doing this in several different reading for the Actual and Theoretical discharge are obtained. Which is
return gives us the different reading for the co-efficient of discharge Cd. First of all we calculate the
values of Qa ,Qt, and Cd.
Diameter= 50
Length =3m
LL =42
RL=29
Head loss=163.7999
D1=5cm
D2=2.72cm
Time=12sec
Qact=281.5cm3
/sec
Qth=3448.5cm3
/sec
Cd=0.82

25. Diameter= 40mm
Length =3m
LL =41.1
RL=25.9
Headloss=191.52cm
D1=4cm
D2=2.366cm
Time=13.3sec
Qact=2537.59cm3
/sec
Qth=2877.1643cm3
/sec
Cd=0.88
Diameter= 20mm
Length =3m
LL =42
RL=40
Headloss=25.2cm
D1=2cm
D2=1.36cm
Time=95sec
Qact=355.2632cm3
/sec
Qth=363.4944cm3
/sec
Cd=0.98
Conclusion
In conclusion the experiment was conducted successfully. As from the results it is evident that the
increase in the flow rate causes the differential head to rise in the two limbs of the manometer
which proves the venturi effect.
References
 https://me.iitp.ac.in
 https://fm-nitk.vlabs.ac.in