Physics · Fluid dynamics. The idea in plain words, the rules to remember, the mistake to avoid and a worked example, written and checked by Mega Lecture.
An ideal fluid is non-viscous, incompressible and in steady flow. Since it cannot be squeezed, the mass entering a pipe each second equals the mass leaving. This gives the equation of continuity: where the pipe is narrow, the fluid moves faster.
Bernoulli's equation is the conservation of energy for a flowing fluid. Pressure, kinetic energy per unit volume and potential energy per unit volume add up to a constant. For a horizontal pipe this means that where the speed is high, the pressure is low.
This one idea explains the speed of water leaving a hole in a tank, the venturi meter, the lift on an aeroplane wing and the paint spray gun.
Area depends on the square of the diameter. If the diameter is halved, the area becomes one quarter and the speed becomes four times as large, not twice.
Answer: 9.0 kPa, with the lower pressure in the narrow section
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