Bernoulli and the Free Jet
Bernoulli and the Free JetObjectives
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.
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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.
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Point 1 is on a vertical line in the jet immediately upstream
from the stagnation point, point 2. The stagnation pressure, , will
be measured using a pressure transducer. Since and are zero and we
can obtain
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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 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
?
3) Measure the jet flow rate using the 7-kPa pressure sensor
connected to the volumetric detector. Log the data to file and with
the pump running turn the jet so it discharges into 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 Bernoullis
equation.
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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).
Figure MACROBUTTON MTPlaceRef \* MERGEFORMAT SEQ MTEqn \h \*
MERGEFORMAT SEQ MTSec \c \* Arabic \* MERGEFORMAT 1- SEQ Figure \s1
\* Arabic \* MERGEFORMAT 2.Stagnation tube and pressure sensor used
to measure velocity in a jet
EMBED Mathcad
Figure MACROBUTTON MTPlaceRef \* MERGEFORMAT SEQ MTEqn \h \*
MERGEFORMAT SEQ MTSec \c \* Arabic \* MERGEFORMAT 1- SEQ Figure \s1
\* Arabic \* MERGEFORMAT 1. Velocity as a function of stagnation
pressure for water.
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