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ME 313-Expt #4 Validation of Bernoulli’s Principle
Purpose: To verify the Bernoulli equation using a Venturi tube.
Apparatus (Bernoulli Principle Demonstration Unit and Hydraulic Bench): Sketch a labeled schematic diagram of the Venturi tube and the interior functions of the hydraulic bench.
Theory: Starting from a fluid element along a streamline derive the Bernoulli equation for steady one-dimensional flow of an incompressible, inviscid fluid:
is the specific weight of the fluid, z is the elevation, V is the velocity on the center streamline in the Venturi tube, P and P0 are the static and stagnation (total) pressure, respectively. Then derive the expression for the velocity V along the streamline as function of P and P0.
From the continuity equation for steady incompressible flow, the mean velocity U at each cross-section of the Venturi tube is:
Q is the volume flow rate, A is the cross-section area.
Procedure
1. Turn on the pump and adjust both the control valve on the hydraulic bench and the valve for the Venturi tube unit alternatively so the tube is filled up with water.
2. Bleed off any air bubbles in the manometers using the valve on the manifold at the top.
3. Adjust the valves to obtain a flow rate so that the total head at the inlet approaches near maximum height on the manometer scale.
4. Place the pitot tube at the inlet of the Venturi tube and read the total head (Manometer #8).
5. Take manometer readings (Manometers #1 – #6) for the static heads at the six cross sections.
6. Close the drain valve at the bottom of the tank of the hydraulic bench. Collect a known volume of water in the tank and record the time required to do so. Repeat this several times to obtain a more reliable average flow rate.
7. Turn off the pump and drain the Venturi tube. Next group of students takes over. Loosen the couplings and reverse the Venturi tube so that the pressure taps are on the divergent duct downstream of the throat.
Purpose: To verify the Bernoulli equation using a Venturi tube.
Apparatus (Bernoulli Principle Demonstration Unit and Hydraulic Bench): Sketch a labeled schematic diagram of the Venturi tube and the interior functions of the hydraulic bench.
Theory: Starting from a fluid element along a streamline derive the Bernoulli equation for steady one-dimensional flow of an incompressible, inviscid fluid:
is the specific weight of the fluid, z is the elevation, V is the velocity on the center streamline in the Venturi tube, P and P0 are the static and stagnation (total) pressure, respectively. Then derive the expression for the velocity V along the streamline as function of P and P0.
From the continuity equation for steady incompressible flow, the mean velocity U at each cross-section of the Venturi tube is:
Q is the volume flow rate, A is the cross-section area.
Procedure
1. Turn on the pump and adjust both the control valve on the hydraulic bench and the valve for the Venturi tube unit alternatively so the tube is filled up with water.
2. Bleed off any air bubbles in the manometers using the valve on the manifold at the top.
3. Adjust the valves to obtain a flow rate so that the total head at the inlet approaches near maximum height on the manometer scale.
4. Place the pitot tube at the inlet of the Venturi tube and read the total head (Manometer #8).
5. Take manometer readings (Manometers #1 – #6) for the static heads at the six cross sections.
6. Close the drain valve at the bottom of the tank of the hydraulic bench. Collect a known volume of water in the tank and record the time required to do so. Repeat this several times to obtain a more reliable average flow rate.
7. Turn off the pump and drain the Venturi tube. Next group of students takes over. Loosen the couplings and reverse the Venturi tube so that the pressure taps are on the divergent duct downstream of the throat.