Continuity & Bernoulli worksheet with answers

Free printable Continuity & Bernoulli worksheet: 6 problems from easy to exam level, with an answer key. Print it or save it as a PDF.

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1.Easy
v = ?h = 4.5 m

An open water tank drains through a small opening in its side. The free surface is 4.5 m above the opening. Ignoring losses, find the jet velocity v at the opening. Use g = 9.81 m/s².

h = 4.5 mg = 9.81 m/s²
v = m/s
2.Easy
12d1​ = 75 mm, v1​ = 1 m/sd2​ = 50 mm, v2​ = ?

Water flows through a pipe that narrows from 75 mm to 50 mm in diameter. The velocity in the wide section is 1 m/s. Find the velocity v2 in the narrow section.

d1 = 75 mmd2 = 50 mmv1 = 1 m/s
v2 = m/s
3.Medium
v = ?p0​pp0​ − p = 24 kPastagnation point

A pitot-static tube in a water pipe reads a difference of 24 kPa between the stagnation pressure and the static pressure. Find the water velocity v at the tip.

p0 − p = 24 kPaρ = 1000 kg/m³
v = m/s
4.Medium
12d1​ = 75 mm, p1​ = 220 kPad2​ = 50 mm, p2​ = ?

Water flows through a horizontal pipe that narrows from 75 mm to 50 mm. In the wide section the pressure is 220 kPa and the velocity is 2 m/s. Ignoring losses, find the pressure p2 in the narrow section.

d1 = 75 mmd2 = 50 mmp1 = 220 kPav1 = 2 m/sρ = 1000 kg/m³
p2 = kPa
5.Hard
12d1​ = 200 mm, p1​ = 380 kPad2​ = 100 mm, p2​ = ?Δz = 1 m

Water flows up through a pipe that narrows from 200 mm to 100 mm while rising 1 m. At section 1 the pressure is 380 kPa and the velocity is 1.25 m/s. Ignoring losses, find the pressure p2 at section 2.

d1 = 200 mmd2 = 100 mmp1 = 380 kPav1 = 1.25 m/sΔz = 1 mρ = 1000 kg/m³
p2 = kPa
6.Hard
12d1​ = 75 mm, p1​ = 330 kPad2​ = 40 mm, p2​ = ?Δz = 1 m

Water flows up through a pipe that narrows from 75 mm to 40 mm while rising 1 m. At section 1 the pressure is 330 kPa and the velocity is 2.5 m/s. Ignoring losses, find the pressure p2 at section 2.

d1 = 75 mmd2 = 40 mmp1 = 330 kPav1 = 2.5 m/sΔz = 1 mρ = 1000 kg/m³
p2 = kPa

Answer key

  1. 1. v = 9.396 m/s
  2. 2. v2 = 2.25 m/s
  3. 3. v = 6.928 m/s
  4. 4. p2 = 211.9 kPa
  5. 5. p2 = 358.5 kPa
  6. 6. p2 = 284.7 kPa

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