Last Updated 9/18/2006
Bernoulli’s Accessory
Figure 1: Bernoulli's Accessory
Materials Hydraulics Bench, Bernoulli’s Accessory, bicycle pump, purge tube, stopwatch
Bernoulli’s Theory
The Bernoulli Equation The Bernoulli equation represents the conservation of mechanical energy for a steady, incompressible, frictionless flow:
p v 2 p v 2 1 1 z 2 2 z (1) g 2g 1 g 2g 2
Where:
p = static pressure detected at a side hole,
v = fluid velocity, and
z = vertical elevation of the fluid, hence
z1 = z2 for a horizontal tube.
1 of 6 Last Updated 9/18/2006
The equation may be derived from the Euler Equations by integration. It may also be derived from energy conservation principles. However, derivation of the Bernoulli Equation is beyond the scope of this theory.
Other Forms of the Bernoulli Equation
If the tube is horizontal, the difference in height can be disregarded, z1 = z2, hence:
p v 2 p v 2 1 1 2 2 (2) g 2g g 2g
With the Bernoulli’s accessory, the static pressure head p, is measured using a manometer directly from a side hole pressure tapping.
The manometer actually measures the static pressure head, h, in meters which is related to p using the relationship:
p h (3) g
This allows the Bernoulli equation to be written in a revised form, i.e.:
v 2 v 2 h 1 h 2 (4) 1 2g 2 2g
The velocity related portion of the total pressure head is called the dynamic pressure head. This is the pressure cause by the flow of the fluid.
Total Pressure Head The total pressure head, h0, can be measured from a probe with an end hole facing into the flow v 2 such that it brings the flow to rest locally at the probe end. Thus, h0 h (meters) and, 2g 0 0 from the Bernoulli equation, it follows that h1 = h2 .
Velocity Measurement The velocity of the flow is measured by measuring the volume of the flow, V, over a time period, V t. This gives the rate of volume flow as: Q , which in turn gives the velocity of flow v t through a defined area, A, i.e:
Q v v (5) A
2 of 6 Last Updated 9/18/2006
Continuity Equation For an incompressible fluid, conservation of mass requires that volume is also conserved,
3 A1v1 = A2v2 etc. (m /s)
Setup and Priming the System 1. Locate the Hydraulics Bench on the 2B level of the ITL near the door of the Machining Studio and position the Bernoulli’s Accessory from the 2B60 module storage bay on top of it so that the outlet from the flow control valve drains into the upper part of the volumetric tank and the back feet rest on the small shelf along that part of the tank as shown in figure. Use the level on the base to adjust the feet until the apparatus is level.
Figure 2: Accessory Positioning
2. Secure the quick release connector on the inlet pipe to the quick release connector in the top of section of the Hydraulic Bench by pushing down on the ring, inserting the hose, and releasing the ring. Be sure the connection has locked and the ball bearings are not visible (it may take some force to ensure the connection is secure).
3. Turn the flow control valve for BOTH the Hydraulics Bench and the Bernoulli’s Accessory completely off (clockwise rotation). Be careful not to apply too much pressure or the pipe fittings could be damaged.
3 of 6 Last Updated 9/18/2006
Motor Switch
Flow Control Valve
Figure 3: Flow Control Valve and Motor Switch
4. With the motor switch in the OFF position. Make sure that the air bleed screw located at the top of the manometer board is fully closed.
5. Check that the Hydraulics Bench is plugged in and turn the motor switch ON. Confirm pump operation by listening to the motor.
6. Slowly open the flow valve on the Hydraulics Bench about a full turn. The rig should begin filling with water.
7. To purge the air out of the system, place one end of the purge hose, the lose hose attached to the back of the manometer board, over the air connector (just below the air bleed screw) and point the other end into the bench’s tank. With one hand holding the tube around the air connector, slowly open the air bleed screw on the Bernoulli’s Accessory. Water should drain through the tube and push all the air out of the manometer board. It is imperative that all bubbles be removed from the manometers for accurate readings. If you are unsuccessful after a series of attempts, contact a TA.
8. Once the system is purged of air, completely close the air bleed screw. The flow control valve on the Hydraulics Bench should remain open for the rest of the experiment. With the system stabilized, the eight manometer readings should be equal.
9. Remove the hose from the air connector and return it to its hook. Attach the bicycle hand pump in its place on the air connector. To do this, the locking flap on the bicycle pump should be parallel to the pump hose when pushing the pump onto the air connector. Flip the flap down (away from the pump hose) to lock the bicycle pump into place. This will also seal the connection to prevent leaks.
10. Change the static pressure of the system using the hand pump and air bleed screw. Slowly open the air bleed screw and then give about two pumps of air into the system. The goal is
to get the eight manometer readings set at approximately 170 to 180 mm H2O. This will enable readings of the manometers during high flow rates not to drift off the board as some readings will increase while others will decrease.
4 of 6 Last Updated 9/18/2006
11. Once the static pressure reading has been reached, close the air bleed screw. Disconnect the hand pump and remount it behind the Bernoulli’s Accessory. The system is now primed.
Experiment 12. Before taking measurements using the manometer board, first remove the total head probe from the testing part of the venturi. Do this by slowly pulling the probe to the right until the tip of the probe is out of the clear plastic part of the venturi. DO NOT pull the probe out any further as it might get pulled out of its guide hole which is located at the edge of the venturi segment.
13. Slowly open the flow control valve on the Bernoulli’s Accessory to the maximum flow rate that keeps all 8 manometer readings within the limits of the scale. Keep a careful eye on manometers 1 and 5 as these will be the maximum and minimum.
14. Measure the flow rate using the Hydraulic Bench’s volumetric tank and a stopwatch. Do this by plugging the drain with the ball stopper. Then, use the scale on the front of the Hydraulic Bench to measure the volume over time. For large flow rates, start timing when the water level hits the upper zero mark. Lower flow rates can be measured with the lower scale. Measurement should occur over at least 30 seconds to ensure accurate results. Take multiple measurements for your uncertainty analysis.
15. Without changing the flow rate, record the pressures given in mm H 2O from manometers 1- 6. This is your static head.
16. Next, re-insert the probe so that the tip lines up with the pressure tap that corresponds to manometer 1. Record the value for total head as measured using manometer 8. You may need to give a little time for the total head to reach equilibrium after moving it.
17. Continue moving the total head probe to line it up with each of the other five pressure taps and record the total head.
18. When all 6 measurements with the probe have been taken, remove the probe from the testing area as described in step 12 above.
19. Decrease the flow using the flow control valve on the Bernoulli’s Accessory and repeat steps 14-19. Continue repeating these steps for at least three different flow rates.
20. Once your data has been collected, calculate the dynamic head using the flow rate and the venturi dimensions given below. Add this to the static head to get total head. Compare this to the total head measured by total head probe.
5 of 6 Last Updated 9/18/2006
Figure 4: Dimensions of Venturi
6 of 6