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 = 16 L/sv = 1 m/s, d = ?

A water line must carry 16 L/s. To limit noise and wear, the mean velocity should be 1 m/s. Find the inner pipe diameter d needed.

Q = 16 L/sv = 1 m/s
d = mm
2.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
3.Medium
12d1​ = 100 mm, p1​ = 170 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 170 kPa and the velocity is 1.75 m/s. Ignoring losses, find the pressure p2 in the narrow section.

d1 = 100 mmd2 = 75 mmp1 = 170 kPav1 = 1.75 m/sρ = 1000 kg/m³
p2 = kPa
4.Medium
v = ?p0​pp0​ − p = 1350 Pastagnation point

A pitot-static tube in a wind tunnel reads a difference of 1350 Pa between the stagnation pressure and the static pressure. The air density is 1.2 kg/m³. Find the air speed v.

p0 − p = 1350 Paρ = 1.2 kg/m³
v = m/s
5.Hard
12d1​ = 100 mm, p1​ = 150 kPad2​ = 50 mm, p2​ = ?Δz = 2 m

Water flows up through a pipe that narrows from 100 mm to 50 mm while rising 2 m. At section 1 the pressure is 150 kPa and the velocity is 0.75 m/s. Ignoring losses, find the pressure p2 at section 2.

d1 = 100 mmd2 = 50 mmp1 = 150 kPav1 = 0.75 m/sΔz = 2 mρ = 1000 kg/m³
p2 = kPa
6.Hard
12d1​ = 75 mm, p1​ = 300 kPad2​ = 40 mm, p2​ = ?Δz = 10 m

Water flows up through a pipe that narrows from 75 mm to 40 mm while rising 10 m. At section 1 the pressure is 300 kPa and the velocity is 1.25 m/s. Ignoring losses, find the pressure p2 at section 2.

d1 = 75 mmd2 = 40 mmp1 = 300 kPav1 = 1.25 m/sΔz = 10 mρ = 1000 kg/m³
p2 = kPa

Answer key

  1. 1. d = 142.7 mm
  2. 2. v = 6.264 m/s
  3. 3. p2 = 166.7 kPa
  4. 4. v = 47.43 m/s
  5. 5. p2 = 126.2 kPa
  6. 6. p2 = 193 kPa

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