CE 321
Lab # 3
Bernoulli’s Equation
General Info:
- Hand in Pre-lab Questions
- Worksheet and Spreadsheets (sent by email) due Thursday by 5 pm
- Lab Reports due Tuesday by 5 pm (both Hardcopy and Electronic)
- www.egr.msu.edu/cee/techcomm
Experiment
Objectives:
1- to investigate the validity of Bernoulli’s equation as applied to a tapering
horizontal zone
2- to determine if the variations in pressure can be predicted by Bernoulli’s equation
for tapering horizontal zone.
Theory
Bernoulli’s Equation:
V12 P1
V2 P
  z1  2  2  z2
2g 
2g 
(1)
If horizontal tube leveled correctly, then z1= z2, and Equation 1 is then simplified to
V12 P1
V2 P
  z1  2  2  z2
2g 
2g 
P1

V12 P1 V22 P2
 

2g  2g 
 pressure head or static head = hs
V12
 velocity head = hv
2g
V2 P
Total head, hT = hs + hv=

2g 
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(2)
CE 321
Lab # 3
Bernoulli made some assumptions for his equation to work:
1. In viscid flow, constant viscosity (no shear stress in the tube)
2. Flow is steady
3. Points 1 and 2 which you are comparing are in the same streamline
4. density of the fluid is constant
5. System is not accelerating
Keep in mind these assumptions while taking measurements in the lab.
Main Objective: is Bernoulli’s equation validated? Why? or Why not? Any assumptions
violated?
hT1  hT2  hT3  hT4  hT5  hT6
In the Data Sheet: hsm = static head measured and hTm = total head measured
Measurement Points:
Tube Cross Section
A
B
0.00
50.00
Convergin
g
CD
E
F
100.00 Position Along Tube (m m )
Diverging
Piezometer: reads static heads or pressure heads
Pitot Probe: total head
Volume will be taken using a volume of 5 L (because of time concerns)
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CE 321
Lab # 3
Analysis:
Follow in coursepack
A. Find Q = V/t (in table 1)
V12
B. Calculate velocity head : hvc =
2g
were V = Q/A, the area of the tube is given in
the spreadsheet
C. Total head best estimate: is the 1st measurement of total head taken at point A
(hTA) for each flow rate.
a. Is the total head constant?
b. Converging different from diverging?
c. Compare total head calculated by Bernoulli to the total head measured at
each point.
D. Predict hsc : hsc = hTm- hvc (from part B); hsc is the static head calculated, hTm is the
total head measured, and hvc is the calculated velocity head.
E. Make graphs in excel: show total measured head, static head and velocity head,
compare total head measured to the total head nest estimate; compare static head
measured to the calculated
F. Converging Section (points A-E):
a. Describe how htm varied in converging section (trends)
b. How does total head best estimate compare to the measured total head
c. Are all assumptions satisfied?
d. Describe the static head measured
e. Compare static head measured to calculated static head
f. Can the static head be predicted by Bernoulli?
G. Do the same analysis for the Diverging Section (points E-F)
H. What happens as flow rate increases or decreases? Describe changes in each
section for total head and static head
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CE 321
Lab # 3
I. Comment on the validity of Bernoulli’s equation for the convergent and divergent
sections.
Tube Cross Section
0.00
50.00
100.00
Position Along Tube (m m )
Eddies form, because of
the sudden expansion
creating shear stress
Velocity increases in the converging zone due to the change in are of the tube; when
the tube diverges the fluid does not contort to the shape of the tube, creating pockets
of “space”. As this space fills up it creates eddies and shear stress, causing the fluid to
lose energy in the process, creating a head loss.
REPORT:
Combine Results and discussion for clarity purposes
Break-up discussion using the objectives for the converging and diverging portions of
the tube.
2 Objectives = 2 conclusions (broken into parts each)
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