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 = 50 L/sv = 1.5 m/s, d = ?

A water line must carry 50 L/s. To limit noise and wear, the mean velocity should be 1.5 m/s. Find the inner pipe diameter d needed.

Q = 50 L/sv = 1.5 m/s
d = mm
2.Easy
12Q = 60 L/sv = 1 m/s, d = ?

A water line must carry 60 L/s. To limit noise and wear, the mean velocity should be 1 m/s. Find the inner pipe diameter d needed.

Q = 60 L/sv = 1 m/s
d = mm
3.Medium
v = ?p0​pp0​ − p = 1450 Pastagnation point

A pitot-static tube in a wind tunnel reads a difference of 1450 Pa between the stagnation pressure and the static pressure. The air density is 1.2 kg/m³. Find the air speed v.

p0 − p = 1450 Paρ = 1.2 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​ = 75 mm, p1​ = 220 kPad2​ = 40 mm, p2​ = ?Δz = 6 m

Water flows up through a pipe that narrows from 75 mm to 40 mm while rising 6 m. At section 1 the pressure is 220 kPa and the velocity is 1.25 m/s. Ignoring losses, find the pressure p2 at section 2.

d1 = 75 mmd2 = 40 mmp1 = 220 kPav1 = 1.25 m/sΔz = 6 mρ = 1000 kg/m³
p2 = kPa
6.Hard
12d1​ = 100 mm, p1​ = 230 kPad2​ = 50 mm, p2​ = ?Δz = 8 m

Water flows up through a pipe that narrows from 100 mm to 50 mm while rising 8 m. At section 1 the pressure is 230 kPa and the velocity is 0.75 m/s. Ignoring losses, find the pressure p2 at section 2.

d1 = 100 mmd2 = 50 mmp1 = 230 kPav1 = 0.75 m/sΔz = 8 mρ = 1000 kg/m³
p2 = kPa

Answer key

  1. 1. d = 206 mm
  2. 2. d = 276.4 mm
  3. 3. v = 49.16 m/s
  4. 4. v = 2.449 m/s
  5. 5. p2 = 152.3 kPa
  6. 6. p2 = 147.3 kPa

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