NUST NET Physics · Physics · Mechanics. The idea in plain words, the rules to remember, the mistake to avoid and a worked example, written and checked by Mega Lecture.
Viscosity is friction inside a fluid. A small sphere moving slowly through a fluid feels a drag given by Stokes' law, which grows with speed. A falling sphere therefore speeds up until drag balances its weight, then falls at a steady terminal velocity.
For an ideal fluid (incompressible, non-viscous, in steady streamline flow) two conservation laws do all the work. Conservation of mass gives the equation of continuity: the fluid moves faster where the pipe is narrower. Conservation of energy gives Bernoulli's equation: where the speed is higher, the pressure is lower. This explains the lift on a wing, the Venturi meter and the speed of water leaving a hole in a tank.
Halving the diameter of a pipe and doubling the speed. Area depends on diameter squared, so half the diameter means a quarter of the area and four times the speed.
Answer: 3.0 × 104 Pa
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