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
12d1​ = 200 mm, v1​ = 0.5 m/sd2​ = 40 mm

Water flows at 0.5 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 = 40 mmv1 = 0.5 m/s
Q = L/s
2.Easy
vd = 15 mmh = 0.5 m

An open water tank drains through a round opening with a diameter of 15 mm in its side. The free surface is 0.5 m above the opening. Ignoring losses and the contraction of the jet, find the flow rate Q. Use g = 9.81 m/s².

h = 0.5 mg = 9.81 m/s²d = 15 mm
Q = L/s
3.Medium
12d1​ = 100 mm, p1​ = ?d2​ = 50 mm, p2​ = 100 kPa

Water flows at 22 L/s through a horizontal pipe that narrows from 100 mm to 50 mm. The pressure in the narrow section is 100 kPa. Ignoring losses, find the pressure p1 in the wide section.

Q = 22 L/sd1 = 100 mmd2 = 50 mmp2 = 100 kPaρ = 1000 kg/m³
p1 = kPa
4.Medium
12d1​ = 75 mm, p1​ = 370 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 370 kPa and the velocity is 2.5 m/s. Ignoring losses, find the pressure p2 in the narrow section.

d1 = 75 mmd2 = 40 mmp1 = 370 kPav1 = 2.5 m/sρ = 1000 kg/m³
p2 = kPa
5.Hard
12d1​ = 75 mm, p1​ = 210 kPad2​ = 50 mm, p2​ = ?Δz = 4 m

Water flows up through a pipe that narrows from 75 mm to 50 mm while rising 4 m. At section 1 the pressure is 210 kPa and the velocity is 1.25 m/s. Ignoring losses, find the pressure p2 at section 2.

d1 = 75 mmd2 = 50 mmp1 = 210 kPav1 = 1.25 m/sΔz = 4 mρ = 1000 kg/m³
p2 = kPa
6.Hard
12d1​ = 75 mm, p1​ = 310 kPad2​ = 25 mm, p2​ = ?Δz = 4 m

Water flows up through a pipe that narrows from 75 mm to 25 mm while rising 4 m. At section 1 the pressure is 310 kPa and the velocity is 1.5 m/s. Ignoring losses, find the pressure p2 at section 2.

d1 = 75 mmd2 = 25 mmp1 = 310 kPav1 = 1.5 m/sΔz = 4 mρ = 1000 kg/m³
p2 = kPa

Answer key

  1. 1. Q = 15.71 L/s
  2. 2. Q = 0.5535 L/s
  3. 3. p1 = 158.8 kPa
  4. 4. p2 = 334.5 kPa
  5. 5. p2 = 167.6 kPa
  6. 6. p2 = 180.8 kPa

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