Bernoulli Theorem Demonstration

To investigate the validity of Bernoulli Equation when applied to the steady flow of water in a tapered duct.


  • The Hydraulics Bench
  • The Bernoulli’s Apparatus Test Equipment
  • Stopwatch


Equipment Set Up

 1)    Level the apparatus

The Bernoulli Equation apparatus is set up on the hydraulic bench so that its base is horizontal; this is necessary for accurate height measurement from the manometers.

2)    Set the direction of the test section

The test section must have the 14° tapered section converging in the direction of flow. If we need to reverse the test section, the total pressure head probe must be withdrawn before releasing the mounting couplings.

3)    Connect the water inlet and outlet

The rig outflow is ensured positioned above the volumetric tank, in order to facilitate timed volume collections. We connect the rig inlet to the bench flow supply; we closed the bench valve and the apparatus flow control valve and we started the pump. Gradually we open the bench valve to fill the test rig with water.

4)    Bleeding the manometers

In order to bleed air from pressure tapping points and manometers, both the bench valve is closed, the ring flow control valve and we open the air bleed screw and we removed the cap from the adjacent air valve. A length of small bore tubing is connected to the volumetric tank. Now, we open the bench valve and we allow flow through the manometers to purge all air from them; then, we tighten the air bleed screw and we partly open the bench valve and test rig flow control valve. Next, the air bleed screw is opened slightly to allow air to enter the top of the manometers (we need to adjust both valves in order to achieve this); we re-tighten the screw when the manometer levels reach a convenient height. We will determined the maximum volume flow rate by the need to have the maximum (h1) and minimum (h5) manometer readings both on scale.

The manometer levels can be adjusted by using the air bleed screw and the hand supplied. The air bleed screw controls the air flow through the air valve, so, when using the hand pump, the bleed screw must be open. We have to retained the hand pump pressure in the system by the screw must be closed after pumping.

Taking a Set of Results

We have to take 3 reading flow rates. Finally, we may reverse the test section in order to see the effects of a more rapid converging section.

1)    Setting the flow rate

First, we take a set of readings at the maximum flow rate, and then we reduce the volume flow rate to give the h1 – h5 difference of about 50mm. Finally, we repeat the whole process for one further flow rate, we set to give the h1 – h5 difference approximately half way between that obtained in the above two tests.

2)    Reading the static head

We take the reading of the h1 – h5 manometers when the levels have steadied. We have to ensure that the total pressure probe is retracted from the test section.

3)    Timed volume collection

We should carry out a timed volume collection, using the volumetric tank, in order to determine the volume flow rate. This we can achieved by closing the ball valve and we measured (with a stopwatch) the time taken to accumulate a known volume of fluid in the tank, which is read from the sight glass. We should collected fluid for a least one minute to minimize timing errors. We also must ensure the total pressure probe should be retraced from the test section during these measurements.

4)    Reading the total pressure head distribution

We measured the total pressure head distribution by traversing the total pressure probe along the length of the test section. The datum line is the side whole pressure tapping associated with the manometer h1. A suitable starting point is 1 cm upstream of the beginning of the 14° tapered section and the measurements should be made at 1 cm intervals along the test section length until the end of the divergent (21°) section.

5)    Reversing the test section

We have to ensure that the total pressure probe is fully withdrawn from the test section (but not pulled out of its guide in the downstream coupling). We unscrew the two couplings, remove the test section and reverse it then re assemble by tightening the coupling. 

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