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 = 2 m

An open water tank drains through a small opening in its side. The free surface is 2 m above the opening. Ignoring losses, find the jet velocity v at the opening. Use g = 9.81 m/s².

h = 2 mg = 9.81 m/s²
v = m/s
2.Easy
v = ?h = 6.5 m

An open water tank drains through a small opening in its side. The free surface is 6.5 m above the opening. Ignoring losses, find the jet velocity v at the opening. Use g = 9.81 m/s².

h = 6.5 mg = 9.81 m/s²
v = m/s
3.Medium
v = ?p0​pp0​ − p = 27 kPastagnation point

A pitot-static tube in a water pipe reads a difference of 27 kPa between the stagnation pressure and the static pressure. Find the water velocity v at the tip.

p0 − p = 27 kPaρ = 1000 kg/m³
v = m/s
4.Medium
12d1​ = 100 mm, p1​ = ?d2​ = 75 mm, p2​ = 120 kPa

Water flows at 12 L/s through a horizontal pipe that narrows from 100 mm to 75 mm. The pressure in the narrow section is 120 kPa. Ignoring losses, find the pressure p1 in the wide section.

Q = 12 L/sd1 = 100 mmd2 = 75 mmp2 = 120 kPaρ = 1000 kg/m³
p1 = kPa
5.Hard
12d1​ = 75 mm, p1​ = 350 kPad2​ = 25 mm, p2​ = ?Δz = 8 m

Water flows up through a pipe that narrows from 75 mm to 25 mm while rising 8 m. At section 1 the pressure is 350 kPa and the velocity is 1 m/s. Ignoring losses, find the pressure p2 at section 2.

d1 = 75 mmd2 = 25 mmp1 = 350 kPav1 = 1 m/sΔz = 8 mρ = 1000 kg/m³
p2 = kPa
6.Hard
12d1​ = 75 mm, p1​ = 400 kPad2​ = 50 mm, p2​ = ?Δz = 6 m

Water flows up through a pipe that narrows from 75 mm to 50 mm while rising 6 m. At section 1 the pressure is 400 kPa and the velocity is 3 m/s. Ignoring losses, find the pressure p2 at section 2.

d1 = 75 mmd2 = 50 mmp1 = 400 kPav1 = 3 m/sΔz = 6 mρ = 1000 kg/m³
p2 = kPa

Answer key

  1. 1. v = 6.264 m/s
  2. 2. v = 11.29 m/s
  3. 3. v = 7.348 m/s
  4. 4. p1 = 122.5 kPa
  5. 5. p2 = 231.5 kPa
  6. 6. p2 = 322.9 kPa

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