Determining the Validity of Bernoulli’s Postulate for Fluid Flow

Lab Report 2

Lab Report

Name

Institution

Table of Contents
Aims 2
Theory 2
Apparatus 2
Assumptions 3
Data/discussion 5
Conclusion 7
References………………………………………………………………………………………………………………………………………………8

Aims
The aim of the experiment is to determine the validity of the Bernoulli’s postulate for fluid flow
THEORY
The motion of a fluid may be described by dividing the fluid into infinite small volume elements which we may call fluid particles and to follow the motion of each particle. If we knew the forces acting on each fluid particle we could then solve for the positions and velocities of each particle as a function of time. The procedure was first developed by Joseph Louise Lagrange (1736-1813) since the fluid particles is generally very large using this task is formidable task.
Apparatus
· Stop watch
· Static pressure manometer
· convergent divergent duct
· Bernoulli’s Apparatus consists essentially of a two dimensional rectangular section convergent divergent duct designed to fit between Cussons P6103 Constant Head Inlet Tank and P6104 Variable Head Outlet Tank.

ASSUMPTIONS
· The fluid is incompressible
· The fluid is nonviscous
· The flow is streamline
· The velocity of the fluid is at any point does not change during the period of observation
Procedure
1. the interior diameter was measured and the cross section area of each test section calculated
2. the distance from the upstream end of the test section to each of the tap locations was measured
3. the pump was started with the bench control valve and outlet control valve closed
4. the valves were gradually opened and adjusted such that the fluid levels in each of the manometers could be clearly read using the permanent scale
5. the flow rate was determined by closing the ball valve in the in the volumetric tank and the time required to accumulate a known volume in the the tank recorded
6. The stagnation probe was retracted though not completely widtdrawnfrom the test section, the fluid level was recorded in each of the five of the manometers . the static pressure head at each tapping point was recorded and the corresponding scale in mm of water
7. The stagnation probe was traversed along the length of the test section and mat each tap,the level of each associated manometer was recorded. The stagnation head represent the total energy head since the velocity at the stagnation point is zero
8. The steps in 4 – 6 were repeated for additional flow rate.

The results were recorded below
Trial one
Volume V,(L)
Time (s)
Volume
Flow rate

5
3.43
0.005
0.14577

Test section
Diameter
(mm)
Distance from test section A
Static pressure head
(mm)
Stagnation pressure head (mm)
Stagnation pressure head
Diameter
(m)
Static pressure head (m)
Stagnation pressure (m)
Cross section area of the flow
Velocity (m/s)
Velocity head
(m)
Total enrgy

A
25

23
25

0.25
0.23
0.25
0.049

B
13.9

21
25

0.139
0.21
0.25
0.015

C
11.8

20
25

0.118
0.20
0.25
0.027

D
10.7

19
25

0.107
0.19
0.25
0.009

E
10

18
25

0.1
0.18
0.25
0.008

Trial two
Volume V,(L)
Time (s)
Volume
Flow rate

5
3.3
0.005
0.0015

Test section
Diameter
(mm)
Distance from test section A
Static pressure head
(mm)
Stagnation pressure head (mm)
Stagnation pressure head
Diameter
(m)
Static pressure head (m)
Stagnation pressure (m)
Cross section area of the flow
Velocity (m/s)
Velocity head
(m)
Total enrgy

A
25
0.3
24.5
24.3
0.243
0.25
0.245
0.243
0.049
0.015
0.01

B
13.9
0.3
19.7
24.3
0.243
0.139
0.197
0.243
0.015
0.015
0.02

C
11.8
0.3
15.3
24.3
0.243
0.118
0.153
0.243
0.027
0.015
0.03

D
11.7
0.3
10.0
24.3
0.243
0.117
0.100
0.243
0.011
0.015
0.04

E
10
0.3
3.0
24.3
0.243
0.10
0.300
0.243
0.008
0.014
0.03

Discussion
Any particle that is under acceleration experiences a net force given by Newton’s second law of motion Newton’s 3 Laws of Motion. (2016). Teachertech.rice.edu. Retrieved 29 September 2016, from http://teachertech.rice.edu/Participants/louviere/Newton/law2.html F=ma if the the velocity of the particle is a function of position and time it may be written as V=V(s,t)
in the case of flowing fluids there is an external friction between the th different layers. This is known as viscous drag or viscous force. When there is shearing the fluid exhibits relative velocity among the layers and cannot remain in equilibrium.

Sources of errors
· poor observation of the stop watch
· observational errors due to parallax
· losses in pipefitting apparatus
Conclusion
We can conclude that energy per unit mass of a fluid is constant along a streamline for steady, incompressible flow of a nonviscous flow. The pressure may vary with time, however but it would have no effect on the flow pattern as stipulated by Bernoulli’s equation.

References
Newton’s 3 Laws of Motion. (2016). Teachertech.rice.edu. Retrieved 29 September 2016, from http://teachertech.rice.edu/Participants/louviere/Newton/law2.html
Upp, E. & LaNasa, P. (2002). Fluid flow measurement. Boston: Gulf Professional Pub.