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
12Q = 55 L/sv = 1.5 m/s, d = ?

A water line must carry 55 L/s. To limit noise and wear, the mean velocity should be 1.5 m/s. Find the inner pipe diameter d needed.

Q = 55 L/sv = 1.5 m/s
d = mm
2.Easy
v = ?h = 7.5 m

An open water tank drains through a small opening in its side. The free surface is 7.5 m above the opening. Ignoring losses, find the jet velocity v at the opening. Use g = 9.81 m/s².

h = 7.5 mg = 9.81 m/s²
v = m/s
3.Medium
12d1​ = 100 mm, p1​ = 190 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 190 kPa and the velocity is 2.75 m/s. Ignoring losses, find the pressure p2 in the narrow section.

d1 = 100 mmd2 = 75 mmp1 = 190 kPav1 = 2.75 m/sρ = 1000 kg/m³
p2 = kPa
4.Medium
12d1​ = 100 mm, p1​ = 230 kPad2​ = 50 mm, p2​ = ?

Water flows through a horizontal pipe that narrows from 100 mm to 50 mm. In the wide section the pressure is 230 kPa and the velocity is 2.75 m/s. Ignoring losses, find the pressure p2 in the narrow section.

d1 = 100 mmd2 = 50 mmp1 = 230 kPav1 = 2.75 m/sρ = 1000 kg/m³
p2 = kPa
5.Hard
12d1​ = 100 mm, p1​ = 300 kPad2​ = 40 mm, p2​ = ?Δz = 5 m

Water flows up through a pipe that narrows from 100 mm to 40 mm while rising 5 m. At section 1 the pressure is 300 kPa and the velocity is 1.5 m/s. Ignoring losses, find the pressure p2 at section 2.

d1 = 100 mmd2 = 40 mmp1 = 300 kPav1 = 1.5 m/sΔz = 5 mρ = 1000 kg/m³
p2 = kPa
6.Hard
12d1​ = 150 mm, p1​ = 240 kPad2​ = 75 mm, p2​ = ?Δz = 4 m

Water flows up through a pipe that narrows from 150 mm to 75 mm while rising 4 m. At section 1 the pressure is 240 kPa and the velocity is 0.5 m/s. Ignoring losses, find the pressure p2 at section 2.

d1 = 150 mmd2 = 75 mmp1 = 240 kPav1 = 0.5 m/sΔz = 4 mρ = 1000 kg/m³
p2 = kPa

Answer key

  1. 1. d = 216.1 mm
  2. 2. v = 12.13 m/s
  3. 3. p2 = 181.8 kPa
  4. 4. p2 = 173.3 kPa
  5. 5. p2 = 208.1 kPa
  6. 6. p2 = 198.9 kPa

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