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 = 11 L/sv = 1.5 m/s, d = ?

A water line must carry 11 L/s. To limit noise and wear, the mean velocity should be 1.5 m/s. Find the inner pipe diameter d needed.

Q = 11 L/sv = 1.5 m/s
d = mm
2.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
3.Medium
v = ?p0​pp0​ − p = 5 kPastagnation point

A pitot-static tube in a water pipe reads a difference of 5 kPa between the stagnation pressure and the static pressure. Find the water velocity v at the tip.

p0 − p = 5 kPaρ = 1000 kg/m³
v = m/s
4.Medium
v = ?p0​pp0​ − p = 3 kPastagnation point

A pitot-static tube in a water pipe reads a difference of 3 kPa between the stagnation pressure and the static pressure. Find the water velocity v at the tip.

p0 − p = 3 kPaρ = 1000 kg/m³
v = m/s
5.Hard
12d1​ = 200 mm, p1​ = 100 kPad2​ = 100 mm, p2​ = ?Δz = 3 m

Water flows up through a pipe that narrows from 200 mm to 100 mm while rising 3 m. At section 1 the pressure is 100 kPa and the velocity is 1.5 m/s. Ignoring losses, find the pressure p2 at section 2.

d1 = 200 mmd2 = 100 mmp1 = 100 kPav1 = 1.5 m/sΔz = 3 mρ = 1000 kg/m³
p2 = kPa
6.Hard
12d1​ = 200 mm, p1​ = 370 kPad2​ = 100 mm, p2​ = ?Δz = 5 m

Water flows up through a pipe that narrows from 200 mm to 100 mm while rising 5 m. At section 1 the pressure is 370 kPa and the velocity is 0.5 m/s. Ignoring losses, find the pressure p2 at section 2.

d1 = 200 mmd2 = 100 mmp1 = 370 kPav1 = 0.5 m/sΔz = 5 mρ = 1000 kg/m³
p2 = kPa

Answer key

  1. 1. d = 96.63 mm
  2. 2. v = 8.859 m/s
  3. 3. v = 3.162 m/s
  4. 4. v = 2.449 m/s
  5. 5. p2 = 53.7 kPa
  6. 6. p2 = 319.1 kPa

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