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 = 52 L/sv = 2 m/s, d = ?

A water line must carry 52 L/s. To limit noise and wear, the mean velocity should be 2 m/s. Find the inner pipe diameter d needed.

Q = 52 L/sv = 2 m/s
d = mm
2.Easy
12Q = 41 L/sv = 2.5 m/s, d = ?

A water line must carry 41 L/s. To limit noise and wear, the mean velocity should be 2.5 m/s. Find the inner pipe diameter d needed.

Q = 41 L/sv = 2.5 m/s
d = mm
3.Medium
12d1​ = 150 mm, p1​ = ?d2​ = 75 mm, p2​ = 70 kPa

Water flows at 20 L/s through a horizontal pipe that narrows from 150 mm to 75 mm. The pressure in the narrow section is 70 kPa. Ignoring losses, find the pressure p1 in the wide section.

Q = 20 L/sd1 = 150 mmd2 = 75 mmp2 = 70 kPaρ = 1000 kg/m³
p1 = kPa
4.Medium
12d1​ = 200 mm, p1​ = 330 kPad2​ = 100 mm, p2​ = ?

Water flows through a horizontal pipe that narrows from 200 mm to 100 mm. In the wide section the pressure is 330 kPa and the velocity is 1.75 m/s. Ignoring losses, find the pressure p2 in the narrow section.

d1 = 200 mmd2 = 100 mmp1 = 330 kPav1 = 1.75 m/sρ = 1000 kg/m³
p2 = kPa
5.Hard
12d1​ = 100 mm, p1​ = 330 kPad2​ = 50 mm, p2​ = ?Δz = 5 m

Water flows up through a pipe that narrows from 100 mm to 50 mm while rising 5 m. At section 1 the pressure is 330 kPa and the velocity is 2.25 m/s. Ignoring losses, find the pressure p2 at section 2.

d1 = 100 mmd2 = 50 mmp1 = 330 kPav1 = 2.25 m/sΔz = 5 mρ = 1000 kg/m³
p2 = kPa
6.Hard
12d1​ = 75 mm, p1​ = 170 kPad2​ = 50 mm, p2​ = ?Δz = 1 m

Water flows up through a pipe that narrows from 75 mm to 50 mm while rising 1 m. At section 1 the pressure is 170 kPa and the velocity is 2 m/s. Ignoring losses, find the pressure p2 at section 2.

d1 = 75 mmd2 = 50 mmp1 = 170 kPav1 = 2 m/sΔz = 1 mρ = 1000 kg/m³
p2 = kPa

Answer key

  1. 1. d = 181.9 mm
  2. 2. d = 144.5 mm
  3. 3. p1 = 79.61 kPa
  4. 4. p2 = 307 kPa
  5. 5. p2 = 243 kPa
  6. 6. p2 = 152.1 kPa

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