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 = 2 m

An open water tank drains through a small opening in its side. The free surface is 2 m above the opening. Ignoring losses, find the jet velocity v at the opening. Use g = 9.81 m/s².

h = 2 mg = 9.81 m/s²
v = m/s
2.Easy
vd = 30 mmh = 6.5 m

An open water tank drains through a round opening with a diameter of 30 mm in its side. The free surface is 6.5 m above the opening. Ignoring losses and the contraction of the jet, find the flow rate Q. Use g = 9.81 m/s².

h = 6.5 mg = 9.81 m/s²d = 30 mm
Q = L/s
3.Medium
12d1​ = 200 mm, p1​ = 300 kPad2​ = 75 mm, p2​ = ?

Water flows through a horizontal pipe that narrows from 200 mm to 75 mm. In the wide section the pressure is 300 kPa and the velocity is 1.75 m/s. Ignoring losses, find the pressure p2 in the narrow section.

d1 = 200 mmd2 = 75 mmp1 = 300 kPav1 = 1.75 m/sρ = 1000 kg/m³
p2 = kPa
4.Medium
12d1​ = 100 mm, p1​ = 400 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 400 kPa and the velocity is 2.5 m/s. Ignoring losses, find the pressure p2 in the narrow section.

d1 = 100 mmd2 = 75 mmp1 = 400 kPav1 = 2.5 m/sρ = 1000 kg/m³
p2 = kPa
5.Hard
12d1​ = 75 mm, p1​ = 330 kPad2​ = 40 mm, p2​ = ?Δz = 1 m

Water flows up through a pipe that narrows from 75 mm to 40 mm while rising 1 m. At section 1 the pressure is 330 kPa and the velocity is 1 m/s. Ignoring losses, find the pressure p2 at section 2.

d1 = 75 mmd2 = 40 mmp1 = 330 kPav1 = 1 m/sΔz = 1 mρ = 1000 kg/m³
p2 = kPa
6.Hard
12d1​ = 75 mm, p1​ = 280 kPad2​ = 25 mm, p2​ = ?Δz = 10 m

Water flows up through a pipe that narrows from 75 mm to 25 mm while rising 10 m. At section 1 the pressure is 280 kPa and the velocity is 1 m/s. Ignoring losses, find the pressure p2 at section 2.

d1 = 75 mmd2 = 25 mmp1 = 280 kPav1 = 1 m/sΔz = 10 mρ = 1000 kg/m³
p2 = kPa

Answer key

  1. 1. v = 6.264 m/s
  2. 2. Q = 7.982 L/s
  3. 3. p2 = 224.1 kPa
  4. 4. p2 = 393.2 kPa
  5. 5. p2 = 314.5 kPa
  6. 6. p2 = 141.9 kPa

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