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 m

An open water tank drains through a small opening in its side. The free surface is 6 m above the opening. Ignoring losses, find the jet velocity v at the opening. Use g = 9.81 m/s².

h = 6 mg = 9.81 m/s²
v = m/s
2.Easy
12Q = 12 L/sv = 1 m/s, d = ?

A water line must carry 12 L/s. To limit noise and wear, the mean velocity should be 1 m/s. Find the inner pipe diameter d needed.

Q = 12 L/sv = 1 m/s
d = mm
3.Medium
d1​ = 150 mmd2​ = 75 mm12p1​ − p2​ = 39 kPaQ = ?

Water flows through a horizontal venturi meter with an inlet diameter of 150 mm and a throat diameter of 75 mm. The pressure at the inlet is 39 kPa higher than at the throat. Ignoring losses, find the flow rate Q.

d1 = 150 mmd2 = 75 mmp1 − p2 = 39 kPaρ = 1000 kg/m³
Q = L/s
4.Medium
12d1​ = 75 mm, p1​ = 350 kPad2​ = 50 mm, p2​ = ?

Water flows through a horizontal pipe that narrows from 75 mm to 50 mm. In the wide section the pressure is 350 kPa and the velocity is 1 m/s. Ignoring losses, find the pressure p2 in the narrow section.

d1 = 75 mmd2 = 50 mmp1 = 350 kPav1 = 1 m/sρ = 1000 kg/m³
p2 = kPa
5.Hard
12d1​ = 100 mm, p1​ = 360 kPad2​ = 75 mm, p2​ = ?Δz = 3 m

Water flows up through a pipe that narrows from 100 mm to 75 mm while rising 3 m. At section 1 the pressure is 360 kPa and the velocity is 2.75 m/s. Ignoring losses, find the pressure p2 at section 2.

d1 = 100 mmd2 = 75 mmp1 = 360 kPav1 = 2.75 m/sΔz = 3 mρ = 1000 kg/m³
p2 = kPa
6.Hard
12d1​ = 100 mm, p1​ = 370 kPad2​ = 75 mm, p2​ = ?Δz = 8 m

Water flows up through a pipe that narrows from 100 mm to 75 mm while rising 8 m. At section 1 the pressure is 370 kPa and the velocity is 2.25 m/s. Ignoring losses, find the pressure p2 at section 2.

d1 = 100 mmd2 = 75 mmp1 = 370 kPav1 = 2.25 m/sΔz = 8 mρ = 1000 kg/m³
p2 = kPa

Answer key

  1. 1. v = 10.85 m/s
  2. 2. d = 123.6 mm
  3. 3. Q = 40.3 L/s
  4. 4. p2 = 348 kPa
  5. 5. p2 = 322.4 kPa
  6. 6. p2 = 286.1 kPa

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