State Bernoulli's theorem and the assumptions on which it rests. Explain two of its uses: the lift on an aircraft wing and the working of a sprayer.

1. 1 · State the theorem. For streamline flow, P + ½ρv² + ρgh is constant along a streamline: where the speed is high, the pressure is low.
2. 2 · Name the terms. P is the pressure energy, ½ρv² the kinetic energy and ρgh the potential energy, each per unit volume.
3. 3 · List the assumptions.
   • The fluid is incompressible.
   • The fluid is non-viscous.
   • The flow is streamlined (steady).
4. 4 · Draw the wing. An aerofoil with streamlines crowded above it and spread out below; mark the speed above as larger and the pressure above as lower.
5. 5 · Explain lift. Faster air above means lower pressure above. The higher pressure below pushes the wing up.
6. 6 · Explain the sprayer. A fast air jet across the top of a thin tube lowers the pressure there. The liquid rises up the tube and is blown out as a fine spray.
7. 7 · Real life. In a storm, fast wind over a tin roof lowers the pressure above it, and the roof lifts off.
8. 8 · Close in one line. Bernoulli's theorem is the conservation of energy for a flowing fluid.

Scoring tip: Draw the streamlines closer together above the wing. That one detail shows the examiner you know where the speed is higher.