Continuity and Bernoulli's Equation for Ideal Flow · seed 1 · A4, ink-friendly. The answer key prints on its own page for grown-ups.
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One flow, one energy budget

Science · Forces & Motion · ages 19-20
Name ______________________   Date ____________

  1. Steady incompressible flow fills a pipe of cross-section 6 square metres at 2 m/s. The pipe narrows to 3 square metres. What is the new speed in m/s?

    Answer: ______________

  2. Water flows through a pipe that narrows halfway along. What happens to the speed in the narrow section?

    • It slows down
    • It speeds up
    • It stays the same

  3. Bernoulli's equation is derived from what idea?

    • Work done on a fluid element
    • Heat lost through the pipe walls
    • Friction between molecules

  4. Air flows faster over the top of a wing than under it, at about the same height. What does Bernoulli's equation say about the pressures?

    • Lower pressure below the wing pushes it down
    • Higher speed above means lower pressure above, so pressure below pushes up
    • Equal speeds above and below cancel out

  5. A level Venturi meter narrows a pipe to measure flow. What happens in the narrow throat?

    • The pressure rises in the throat
    • The speed drops in the throat
    • The pressure drops in the throat

  6. A river carries a steady flow with no water added or taken away. Its cross-section is 4 square metres where it runs at 3 m/s, then 2 square metres in a gorge. What is the gorge speed in m/s?

    Answer: ______________

  7. An open tank drains through a hole near its base. The deeper the fluid above the hole, the faster the exit jet. True or false?

    Circle one:   True   False

  8. Where does Bernoulli's equation fail, and why?

    • Long thin pipes with sticky viscous losses
    • Short wide pipes with smooth steady flow
    • A Venturi throat with clean fast flow
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Answer key

For grown-ups. Fold this page away before handing over the rest.

One flow, one energy budget W1-mt_pKxlVYTy0Y-s1

  1. 4 · Continuity gives 2 times 6 is 3 times the new speed, so the new speed is 4 m/s.
  2. It speeds up · Whatever flows in must flow out, so a smaller area forces a higher speed.
  3. Work done on a fluid element · Pressure pushes on both ends while gravity may raise the parcel, and the net work becomes kinetic energy.
  4. Higher speed above means lower pressure above, so pressure below pushes up · Faster air over the wing means lower pressure above it, and the pressure below pushes it up.
  5. The pressure drops in the throat · The narrow throat has faster flow and lower pressure, and the pressure drop reveals the flow rate.
  6. 6 · Continuity gives 3 times 4 is 2 times the new speed, so the new speed is 6 m/s.
  7. True · The surface sits higher than the hole, so that height turns into exit speed set by the depth.
  8. Long thin pipes with sticky viscous losses · Viscosity breaks the frictionless assumption, so the equation fails there.
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