Intro to Fluid and Thermal Transport – ME 331
Laboratory Assignment #3
Bernoulli Equation Demonstration
C. J. Kobus
Figure 1 shows the apparatus used to investigate the validity of the Bernoulli equation
when applied to the steady flow of water in a tapered duct. The apparatus consists of a
clear acrylic duct of varying circular
cross section, known as a Venturi. The
duct has a number of side hole pressure
tapings connected to a manometer bank,
which allows the measurement of static
pressure at 6 different sections. The
apparatus is mounted on an Armfield
hydraulics bench and flow control valves
are used to control the flowrate through
the Venturi. Figure 2 and Table 1
respectively show the positions (in mm)
of the pressure tapings and the
dimensions of the cross-sections. The
duct has an upstream taper of 14o and a
downstream taper of 21o.
The objective of this experiment is to evaluate the validity of the Bernoulli equation when
applied to a converging-diverging nozzle.
Table 1 - Dimensions of the Venturi Cross-sections
Tapping Position Diameter of cross-section (mm)
Manometer Height
A
25.0
h1
B
13.9
h2
C
11.8
h3
D
10.7
h4
E
10.0
h5
F
25.0
h6
1.
2.
Photo from Armfield Hydraulics Bench and Accessories catalog : http://www.armfield.co.uk
Schematic from Armfield “Bernoulli’s Theorem Demonstration, F1-15” Instruction Manual, Issue
4, September 2001.
INTRODUCTION TO FLUID AND THERMAL ENERGY TRANSPORT - ME331
Assignment Specifications
1. Perform an experiment to measure the steady manometer deflections at the 6
pressure tapings for three inlet volume flowrates (1.0 gpm, 1.5 gpm, and 2.0 gpm).
The manometer levels can be adjusted using a hand pump and an air bleed screw
until they reach a convenient height. Start with the highest flowrate, record the
steady manometer levels then repeat for the next lower flowrate.
2. Plot the static pressure deflection (hi-h6) as a function of position number, i, for
the three flowrates. Discuss the effect of flowrate on the pressure drop through the
duct.
3. Assuming steady and incompressible flow and using the conservation of mass
equation, the velocity, Vi, at each tap location, i, can be determined from the
volume flowrate as
/A
Vi  
i
where Ai is the cross-sectional area at tap i. For each flowrate, calculate and plot
these velocities (m/s) as a function of position number, i.
4. Using Bernoulli’s Equation for incompressible, inviscid flow and the manometer
equation, derive an expression relating the velocity at each tap location to the
manometer height measurements at a cross section and to the velocity at tap A.
5. Superimpose the velocities predicted by the Bernoulli equation on the plots from
spec. #3. For tap A use the velocity determined using eq. (1).
6. Perform an uncertainty analysis on the velocity calculations from eq. (1) and
show error bars on the plots. Perform a sensitivity analysis on the Bernoulli
equation velocity predictions and include error bands on the plots. Assume the
following accuracy for the direct measurements: diameter = ± 0.05 mm,
manometer level = ±2.5 mm, flowrate = ± 3% f.s.f.
7. Compare the velocity predictions from the Bernoulli equation to those calculated
using eq. (1). Discuss any discrepancies and comment on the agreement between
your theoretical and experimental results.
8. A venturi is a device that is sometimes used to measure flowrate. The volume
flowrate is determined by measuring the pressure difference between the upstream
section and the throat of the nozzle. Using Bernoulli’s Equation for
incompressible, inviscid flow, the manometer equation, and the conservation of
mass equation, show that that the volume flowrate can be predicted by
1

 2
d 52
d12
 2 g (h1  h5 ) 

  A5 
 , where A1   4 and A5   4
A
2
1  ( 5 A ) 
1


Compare this prediction to your directly measured volume flowrates.