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 = 15 L/sv = 1.5 m/s, d = ?

A water line must carry 15 L/s. To limit noise and wear, the mean velocity should be 1.5 m/s. Find the inner pipe diameter d needed.

Q = 15 L/sv = 1.5 m/s
d = mm
2.Easy
12d1​ = 200 mm, v1​ = 1.5 m/sd2​ = 75 mm

Water flows at 1.5 m/s through the wide section of the pipe, which has a diameter of 200 mm. Find the volume flow rate Q.

d1 = 200 mmd2 = 75 mmv1 = 1.5 m/s
Q = L/s
3.Medium
12d1​ = 100 mm, p1​ = 130 kPad2​ = 75 mm, p2​ = ?

Water flows through a horizontal pipe that narrows from 100 mm to 75 mm. In the wide section the pressure is 130 kPa and the velocity is 3 m/s. Ignoring losses, find the pressure p2 in the narrow section.

d1 = 100 mmd2 = 75 mmp1 = 130 kPav1 = 3 m/sρ = 1000 kg/m³
p2 = kPa
4.Medium
12d1​ = 100 mm, p1​ = 100 kPad2​ = 50 mm, p2​ = ?

Water flows through a horizontal pipe that narrows from 100 mm to 50 mm. In the wide section the pressure is 100 kPa and the velocity is 1.5 m/s. Ignoring losses, find the pressure p2 in the narrow section.

d1 = 100 mmd2 = 50 mmp1 = 100 kPav1 = 1.5 m/sρ = 1000 kg/m³
p2 = kPa
5.Hard
12d1​ = 150 mm, p1​ = 110 kPad2​ = 50 mm, p2​ = ?Δz = 3 m

Water flows up through a pipe that narrows from 150 mm to 50 mm while rising 3 m. At section 1 the pressure is 110 kPa and the velocity is 0.5 m/s. Ignoring losses, find the pressure p2 at section 2.

d1 = 150 mmd2 = 50 mmp1 = 110 kPav1 = 0.5 m/sΔz = 3 mρ = 1000 kg/m³
p2 = kPa
6.Hard
12d1​ = 100 mm, p1​ = 380 kPad2​ = 75 mm, p2​ = ?Δz = 2 m

Water flows up through a pipe that narrows from 100 mm to 75 mm while rising 2 m. At section 1 the pressure is 380 kPa and the velocity is 1 m/s. Ignoring losses, find the pressure p2 at section 2.

d1 = 100 mmd2 = 75 mmp1 = 380 kPav1 = 1 m/sΔz = 2 mρ = 1000 kg/m³
p2 = kPa

Answer key

  1. 1. d = 112.8 mm
  2. 2. Q = 47.12 L/s
  3. 3. p2 = 120.3 kPa
  4. 4. p2 = 83.13 kPa
  5. 5. p2 = 70.57 kPa
  6. 6. p2 = 359.3 kPa

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