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
v = ?h = 6.5 m

An open water tank drains through a small opening in its side. The free surface is 6.5 m above the opening. Ignoring losses, find the jet velocity v at the opening. Use g = 9.81 m/s².

h = 6.5 mg = 9.81 m/s²
v = m/s
2.Easy
12d1​ = 150 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 150 mm. Find the volume flow rate Q.

d1 = 150 mmd2 = 75 mmv1 = 1.5 m/s
Q = L/s
3.Medium
12d1​ = 100 mm, p1​ = ?d2​ = 50 mm, p2​ = 90 kPa

Water flows at 10 L/s through a horizontal pipe that narrows from 100 mm to 50 mm. The pressure in the narrow section is 90 kPa. Ignoring losses, find the pressure p1 in the wide section.

Q = 10 L/sd1 = 100 mmd2 = 50 mmp2 = 90 kPaρ = 1000 kg/m³
p1 = kPa
4.Medium
12d1​ = 100 mm, p1​ = 160 kPad2​ = 25 mm, p2​ = ?

Water flows through a horizontal pipe that narrows from 100 mm to 25 mm. In the wide section the pressure is 160 kPa and the velocity is 0.75 m/s. Ignoring losses, find the pressure p2 in the narrow section.

d1 = 100 mmd2 = 25 mmp1 = 160 kPav1 = 0.75 m/sρ = 1000 kg/m³
p2 = kPa
5.Hard
12d1​ = 150 mm, p1​ = 320 kPad2​ = 75 mm, p2​ = ?Δz = 2 m

Water flows up through a pipe that narrows from 150 mm to 75 mm while rising 2 m. At section 1 the pressure is 320 kPa and the velocity is 1.25 m/s. Ignoring losses, find the pressure p2 at section 2.

d1 = 150 mmd2 = 75 mmp1 = 320 kPav1 = 1.25 m/sΔz = 2 mρ = 1000 kg/m³
p2 = kPa
6.Hard
12d1​ = 100 mm, p1​ = 230 kPad2​ = 25 mm, p2​ = ?Δz = 2 m

Water flows up through a pipe that narrows from 100 mm to 25 mm while rising 2 m. At section 1 the pressure is 230 kPa and the velocity is 0.5 m/s. Ignoring losses, find the pressure p2 at section 2.

d1 = 100 mmd2 = 25 mmp1 = 230 kPav1 = 0.5 m/sΔz = 2 mρ = 1000 kg/m³
p2 = kPa

Answer key

  1. 1. v = 11.29 m/s
  2. 2. Q = 26.51 L/s
  3. 3. p1 = 102.2 kPa
  4. 4. p2 = 88.28 kPa
  5. 5. p2 = 288.7 kPa
  6. 6. p2 = 178.5 kPa

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