Bernoulli and the Free Jet
Objectives
In this laboratory you will measure fluid velocities in a free jet using a stagnation tube. You
will confirm that the Bernoulli equation can be used to measure fluid velocities using a simple
stagnation tube.
Theory
The conservation of mechanical energy will be verified using the Bernoulli equation.
p


V2
z C
2g
1.1
A stagnation tube will be connected to a pressure sensor. The stagnation tube will be filled with
water prior to connecting to the pressure sensor and the pressure sensor output will be zeroed with
the stagnation tube held vertically (in the same orientation used for taking measurements.) Thus
the pressure sensor will measure the pressure at the stagnation point (Figure 1-2). From the
Bernoulli equation we can obtain the following relationship.
p1

 z1 
V12 p2
V2

 z2  2
2g 
2g
1.2
Point 1 is on a vertical line in the jet immediately upstream from the stagnation point, point 2.
V22
The stagnation pressure, p2 , will be measured using a pressure transducer. Since
and

2g
are zero and z1  z2 we can obtain
p1
V1 
2 p2

1.3
Thus by measuring the stagnation pressure we can calculate the velocity of the jet (Figure
1-1).
Experimental Methods and Analysis
Set up a small jet powered by a
centrifugal pump connected to the 10 cm
diameter column. Install a valve between
the effluent of the centrifugal pump and
the elbow. Install a 7 kPa pressure sensor
in the bottom of the 10 cm diameter
column. Fill the 10 cm diameter column
with 15 cm of water. Fill the stagnation
tube completely with water before
connecting the 7 kPa pressure sensor.
Monitor the pressure sensors with the
Process Controller software and apply
scaling so the output is measured in
Pascals for the stagnation tube and in mL
4
3
V( p )
2
m
1
s
0
0
1400
2800
4200
p
Figure 1-1.
Velocity as
stagnation pressure for water.
5600
7000
Pressure in Pa
a
function
of
of water for the 10 cm diameter column. Zero the
output of the stagnation tube pressure sensor with
the stagnation tube held vertically in air.
Set the flow rate using the valve so the
stagnation pressure at z = 0 is approximately 300
Pa.
Make the following measurements and
calculations.
1) What is the stagnation pressure at z = 0?
2) What is the velocity at z = 0 obtained using
equation 1.3?
SS Tubing with
7.25 mm ID
7 kPa Pressure
Sensor z
Free Jet
Stagnation
Point
Stagnation
Tube filled
with water
Centrifugal
Pump
3) Measure the jet flow rate using the 7-kPa
pressure sensor connected to the volumetric
Figure 1-2.
Stagnation tube and
detector. Log the data to file and with the
pressure sensor used to measure
pump running turn the jet so it discharges into
velocity in a jet
a different container. You will use the initial
slope of the resulting data to determine the
flow rate out of the volumetric detector.
4) What is the flow rate that you obtain from the initial slope and how does it compare with the
flow rate calculated using the stagnation tube?
5) Fill the volumetric detector to 15 cm again and measure the stagnation tube pressure at
various elevations in the jet. Use Excel to plot the velocity in the jet as a function of
elevation. On the same graph plot the prediction based on Bernoulli’s equation.
z1 
V12
V2
 z2  2
2g
2g
1.6
where points one and two are any two points in a free jet. Make sure that the theoretical
model is plotted as a smooth curve. Format the graphs (from 3 and 5) correctly
(http://ceeserver.cee.cornell.edu/mw24/cee331/lab_report.htm#graphs ). Insert a textbox
or Word object into Excel and summarize what you learned and your suggestions for
improving this laboratory exercise. Email the Excel file to the TA and to the Instructor.
Lab Setup
1) Plug both 7 kPa pressure sensors into the middle row of ports.
2) Make sure the middle row of ports is configured with a maximum voltage of 20 mV.
3) Use the Process Controller to turn on the pump and the solenoid valve attached to the pump.
4) Use #14 Pharmed tubing to connect the pressure sensor to the stagnation tube.
5) Configure the Process Controller at each station so it is monitoring the correct pressure
sensors at each station. Apply the correct conversions to both pressure sensors (Pa for the
stagnation tube and mL of water for the 10 cm diameter column).