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 = 6 L/sv = 2.5 m/s, d = ?

A water line must carry 6 L/s. To limit noise and wear, the mean velocity should be 2.5 m/s. Find the inner pipe diameter d needed.

Q = 6 L/sv = 2.5 m/s
d = mm
2.Easy
v = ?h = 0.5 m

An open water tank drains through a small opening in its side. The free surface is 0.5 m above the opening. Ignoring losses, find the jet velocity v at the opening. Use g = 9.81 m/s².

h = 0.5 mg = 9.81 m/s²
v = m/s
3.Medium
12d1​ = 200 mm, p1​ = ?d2​ = 150 mm, p2​ = 140 kPa

Water flows at 35 L/s through a horizontal pipe that narrows from 200 mm to 150 mm. The pressure in the narrow section is 140 kPa. Ignoring losses, find the pressure p1 in the wide section.

Q = 35 L/sd1 = 200 mmd2 = 150 mmp2 = 140 kPaρ = 1000 kg/m³
p1 = kPa
4.Medium
12d1​ = 200 mm, p1​ = 310 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 310 kPa and the velocity is 2.25 m/s. Ignoring losses, find the pressure p2 in the narrow section.

d1 = 200 mmd2 = 100 mmp1 = 310 kPav1 = 2.25 m/sρ = 1000 kg/m³
p2 = kPa
5.Hard
12d1​ = 75 mm, p1​ = 120 kPad2​ = 50 mm, p2​ = ?Δz = 8 m

Water flows up through a pipe that narrows from 75 mm to 50 mm while rising 8 m. At section 1 the pressure is 120 kPa and the velocity is 1.5 m/s. Ignoring losses, find the pressure p2 at section 2.

d1 = 75 mmd2 = 50 mmp1 = 120 kPav1 = 1.5 m/sΔz = 8 mρ = 1000 kg/m³
p2 = kPa
6.Hard
12d1​ = 150 mm, p1​ = 200 kPad2​ = 75 mm, p2​ = ?Δz = 8 m

Water flows up through a pipe that narrows from 150 mm to 75 mm while rising 8 m. At section 1 the pressure is 200 kPa and the velocity is 2 m/s. Ignoring losses, find the pressure p2 at section 2.

d1 = 150 mmd2 = 75 mmp1 = 200 kPav1 = 2 m/sΔz = 8 mρ = 1000 kg/m³
p2 = kPa

Answer key

  1. 1. d = 55.28 mm
  2. 2. v = 3.132 m/s
  3. 3. p1 = 141.3 kPa
  4. 4. p2 = 272 kPa
  5. 5. p2 = 36.95 kPa
  6. 6. p2 = 91.52 kPa

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