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
12d1​ = 100 mm, v1​ = 1.25 m/sd2​ = 75 mm, v2​ = ?

Water flows through a pipe that narrows from 100 mm to 75 mm in diameter. The velocity in the wide section is 1.25 m/s. Find the velocity v2 in the narrow section.

d1 = 100 mmd2 = 75 mmv1 = 1.25 m/s
v2 = m/s
2.Easy
12Q = 13 L/sv = 1.5 m/s, d = ?

A water line must carry 13 L/s. To limit noise and wear, the mean velocity should be 1.5 m/s. Find the inner pipe diameter d needed.

Q = 13 L/sv = 1.5 m/s
d = mm
3.Medium
12d1​ = 100 mm, p1​ = 140 kPad2​ = 40 mm, p2​ = ?

Water flows through a horizontal pipe that narrows from 100 mm to 40 mm. In the wide section the pressure is 140 kPa and the velocity is 2 m/s. Ignoring losses, find the pressure p2 in the narrow section.

d1 = 100 mmd2 = 40 mmp1 = 140 kPav1 = 2 m/sρ = 1000 kg/m³
p2 = kPa
4.Medium
v = ?p0​pp0​ − p = 700 Pastagnation point

A pitot-static tube in a wind tunnel reads a difference of 700 Pa between the stagnation pressure and the static pressure. The air density is 1.2 kg/m³. Find the air speed v.

p0 − p = 700 Paρ = 1.2 kg/m³
v = m/s
5.Hard
12d1​ = 200 mm, p1​ = 100 kPad2​ = 100 mm, p2​ = ?Δz = 1 m

Water flows up through a pipe that narrows from 200 mm to 100 mm while rising 1 m. At section 1 the pressure is 100 kPa and the velocity is 1.25 m/s. Ignoring losses, find the pressure p2 at section 2.

d1 = 200 mmd2 = 100 mmp1 = 100 kPav1 = 1.25 m/sΔz = 1 mρ = 1000 kg/m³
p2 = kPa
6.Hard
12d1​ = 100 mm, p1​ = 110 kPad2​ = 50 mm, p2​ = ?Δz = 3 m

Water flows up through a pipe that narrows from 100 mm to 50 mm while rising 3 m. At section 1 the pressure is 110 kPa and the velocity is 1.25 m/s. Ignoring losses, find the pressure p2 at section 2.

d1 = 100 mmd2 = 50 mmp1 = 110 kPav1 = 1.25 m/sΔz = 3 mρ = 1000 kg/m³
p2 = kPa

Answer key

  1. 1. v2 = 2.222 m/s
  2. 2. d = 105 mm
  3. 3. p2 = 63.88 kPa
  4. 4. v = 34.16 m/s
  5. 5. p2 = 78.47 kPa
  6. 6. p2 = 68.85 kPa

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