Bernoulli principle

Class practical

In a streamline flow, fluid pressure will be reduced in a region where the flow velocity is increased, for example due to a constriction.

Apparatus and Materials

• Bernoulli tubes (also called Venturi tubes).
• Rubber tubing
• Funnel
• Air pump
• Ping pong ball or other light ball

Depending on the supplier, ‘Bernoulli tubes’ may come as a single tube with a narrower cross-section in its middle, or as two tubes, (one with a constant cross-section and the other with a narrower cross-section in its middle). Each tube will have connectors, to which you attach manometers at 3 positions. The tubes and manometers will need to be clamped to stands, near a sink for water source and drain.

Suppliers of Bernoulli tubes include the following: EDU-LAB, Eisco Labs, and PASCO Scientific.

Health & Safety and Technical Notes

Take care when handling and clamping the Bernoulli tubes, fragile glassware. Be careful not to get water on the floor, which can create a slip hazard.

Read our standard health & safety guidance

Procedure

1. If you have tubing of constant cross-section, run water through it and discuss the relative heights of the 3 manometers.

2. After asking students to predict (with some explanation) what might happen with the tubing that has a narrower cross-section in the middle, run water through it. The middle manometer will be lower than the other two.

3. Ask students to predict what may happen if air is blown out through the funnel, above a light ball. Then try it.

Teaching Notes

• In steps 1 and 2 water flows steadily along the tube with no turbulence. In step 3 air similarly moves smoothly through the funnel. In all cases, the flow is described as ‘streamline’.
• In step 1, with a tube of uniform diameter, the levels in the three manometers decrease slightly along the direction of flow. This shows that there is a slight decrease in pressure along the tube. This pressure difference is needed to overcome viscous drag along the tubing walls.
• In step 2, the mass flow rate of the water is the same in the narrow central section of the tube as in the outer sections. The level in the central manometer is lower than that in the other two manometers, showing that the pressure is less where the water is flowing faster.
• The pressure difference between the first two manometers is needed to accelerate the water as it enters the narrow tube. Similarly, the increase in pressure between the second and third manometers causes the water to decelerate as it enters the wider tube.
• Bernoulli’s equation relates the pressure P and speed v of a fluid along a streamline. For horizontal flow (no change in gravitational potential energy) we have: P 2 < P 1 because v 2 > v 1
• In step 3, the air slows down and its pressure increases as it moves from the narrow tube to the wider funnel. The ball is pushed from the area of higher pressure towards the area of lower pressure.
• Note that many controversial or false demonstrations of the Bernoulli principle are prevalent, for example aerofoil lift, balls in curving flight, or lifting a sheet of paper by blowing across its upper surface.

This experiment has yet to undergo a health and safety check.