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
12Q = 13 L/sv = 2.5 m/s, d = ?

A water line must carry 13 L/s. To limit noise and wear, the mean velocity should be 2.5 m/s. Find the inner pipe diameter d needed.

Q = 13 L/sv = 2.5 m/s
d = mm
2.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
3.Medium
12d1​ = 200 mm, p1​ = ?d2​ = 150 mm, p2​ = 60 kPa

Water flows at 22 L/s through a horizontal pipe that narrows from 200 mm to 150 mm. The pressure in the narrow section is 60 kPa. Ignoring losses, find the pressure p1 in the wide section.

Q = 22 L/sd1 = 200 mmd2 = 150 mmp2 = 60 kPaρ = 1000 kg/m³
p1 = kPa
4.Medium
12d1​ = 75 mm, p1​ = 240 kPad2​ = 40 mm, p2​ = ?

Water flows through a horizontal pipe that narrows from 75 mm to 40 mm. In the wide section the pressure is 240 kPa and the velocity is 2.5 m/s. Ignoring losses, find the pressure p2 in the narrow section.

d1 = 75 mmd2 = 40 mmp1 = 240 kPav1 = 2.5 m/sρ = 1000 kg/m³
p2 = kPa
5.Hard
12d1​ = 75 mm, p1​ = 260 kPad2​ = 40 mm, p2​ = ?Δz = 10 m

Water flows up through a pipe that narrows from 75 mm to 40 mm while rising 10 m. At section 1 the pressure is 260 kPa and the velocity is 0.75 m/s. Ignoring losses, find the pressure p2 at section 2.

d1 = 75 mmd2 = 40 mmp1 = 260 kPav1 = 0.75 m/sΔz = 10 mρ = 1000 kg/m³
p2 = kPa
6.Hard
12d1​ = 150 mm, p1​ = 270 kPad2​ = 40 mm, p2​ = ?Δz = 5 m

Water flows up through a pipe that narrows from 150 mm to 40 mm while rising 5 m. At section 1 the pressure is 270 kPa and the velocity is 1 m/s. Ignoring losses, find the pressure p2 at section 2.

d1 = 150 mmd2 = 40 mmp1 = 270 kPav1 = 1 m/sΔz = 5 mρ = 1000 kg/m³
p2 = kPa

Answer key

  1. 1. d = 81.37 mm
  2. 2. v = 6.264 m/s
  3. 3. p1 = 60.53 kPa
  4. 4. p2 = 204.5 kPa
  5. 5. p2 = 158.7 kPa
  6. 6. p2 = 122.6 kPa

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