AP Physics 1 · Unit 8 · Fluids

Bernoulli’s Principle Practice Problems

Connect pressure, speed, and elevation using continuity and energy per volume, then apply those ideas to tank outflow and fountains.

12 questions6 conceptual · 6 calculation

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Simulation scene from the Bernoulli’s Principle lesson. — A scene from the related lesson. Open the practice to work through the questions.

What you’ll practice

Balance pressure, kinetic, and gravitational terms

Find pressures and nozzle speeds

Combine continuity with Bernoulli’s equation. Account for both the speed change and elevation change, and keep absolute and gauge pressures consistent.

Infer tank head from collected volume

Use a steady collection interval to calculate volume flow, convert opening area to SI units, and apply Torricelli’s relation to find the head above the outlet.

Connect pipe flow to a fountain trajectory

Find the underground supply pressure, then follow a water parcel after it leaves an atmospheric nozzle. Calculate vertical peak height and range for an angled launch.

A question from this set

A horizontal restriction

An ideal, steady, incompressible flow passes into a narrower horizontal pipe section. There is no pump or dissipative loss between the two sections. What happens to the average speed and static pressure?

Speed increases and static pressure decreases.
Both speed and static pressure increase.
Speed is unchanged and pressure decreases only because the pipe is longer.

Try it in the practice set

Compare static pressure and average speed as an ideal flow enters a narrower horizontal section.

Key ideas

Pressure is one part of the energy balance

Slower flow can still have lower pressure

In a widening pipe that also climbs, the decrease in kinetic energy per volume competes with the increase in gravitational energy per volume. Compare both contributions before deciding how pressure changes.

Pressure differences depend on speed squared

For a horizontal restriction with fixed areas and density, doubling volume flow doubles both section speeds and quadruples the required pressure difference. The absolute pressure itself need not quadruple.

See the physics

Compare pipe energy profiles and measured jets

After attempting a question, inspect section pressures, speeds, and energy per volume. Collect a steady jet over a measured interval, compare reservoir heads, and run a fountain to its recorded peak or ground-level landing.

Use a hint for a starting point or open a worked solution to follow the reasoning. Your progress saves in this browser, so you can return to unfinished questions.

Ready for bernoulli’s principle?

Begin with a conceptual question, then work through the calculations.

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