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 = 4 m

An open water tank drains through a small opening in its side. The free surface is 4 m above the opening. Ignoring losses, find the jet velocity v at the opening. Use g = 9.81 m/s².

h = 4 mg = 9.81 m/s²
v = m/s
2.Easy
vd = 20 mmh = 3 m

An open water tank drains through a round opening with a diameter of 20 mm in its side. The free surface is 3 m above the opening. Ignoring losses and the contraction of the jet, find the flow rate Q. Use g = 9.81 m/s².

h = 3 mg = 9.81 m/s²d = 20 mm
Q = L/s
3.Medium
12d1​ = 200 mm, p1​ = 360 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 360 kPa and the velocity is 1 m/s. Ignoring losses, find the pressure p2 in the narrow section.

d1 = 200 mmd2 = 75 mmp1 = 360 kPav1 = 1 m/sρ = 1000 kg/m³
p2 = kPa
4.Medium
d1​ = 100 mmd2​ = 60 mm12p1​ − p2​ = 13 kPaQ = ?

Water flows through a horizontal venturi meter with an inlet diameter of 100 mm and a throat diameter of 60 mm. The pressure at the inlet is 13 kPa higher than at the throat. Ignoring losses, find the flow rate Q.

d1 = 100 mmd2 = 60 mmp1 − p2 = 13 kPaρ = 1000 kg/m³
Q = L/s
5.Hard
12d1​ = 100 mm, p1​ = 400 kPad2​ = 40 mm, p2​ = ?Δz = 2 m

Water flows up through a pipe that narrows from 100 mm to 40 mm while rising 2 m. At section 1 the pressure is 400 kPa and the velocity is 1 m/s. Ignoring losses, find the pressure p2 at section 2.

d1 = 100 mmd2 = 40 mmp1 = 400 kPav1 = 1 m/sΔz = 2 mρ = 1000 kg/m³
p2 = kPa
6.Hard
12d1​ = 75 mm, p1​ = 170 kPad2​ = 50 mm, p2​ = ?Δz = 10 m

Water flows up through a pipe that narrows from 75 mm to 50 mm while rising 10 m. At section 1 the pressure is 170 kPa and the velocity is 1 m/s. Ignoring losses, find the pressure p2 at section 2.

d1 = 75 mmd2 = 50 mmp1 = 170 kPav1 = 1 m/sΔz = 10 mρ = 1000 kg/m³
p2 = kPa

Answer key

  1. 1. v = 8.859 m/s
  2. 2. Q = 2.41 L/s
  3. 3. p2 = 335.2 kPa
  4. 4. Q = 15.45 L/s
  5. 5. p2 = 361.3 kPa
  6. 6. p2 = 69.87 kPa

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