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 = 32 L/sv = 1 m/s, d = ?

A water line must carry 32 L/s. To limit noise and wear, the mean velocity should be 1 m/s. Find the inner pipe diameter d needed.

Q = 32 L/sv = 1 m/s
d = mm
2.Easy
12Q = 48 L/sv = 1.5 m/s, d = ?

A water line must carry 48 L/s. To limit noise and wear, the mean velocity should be 1.5 m/s. Find the inner pipe diameter d needed.

Q = 48 L/sv = 1.5 m/s
d = mm
3.Medium
v = ?p0​pp0​ − p = 650 Pastagnation point

A pitot-static tube in a wind tunnel reads a difference of 650 Pa between the stagnation pressure and the static pressure. The air density is 1.2 kg/m³. Find the air speed v.

p0 − p = 650 Paρ = 1.2 kg/m³
v = m/s
4.Medium
v = ?p0​pp0​ − p = 8 kPastagnation point

A pitot-static tube in a water pipe reads a difference of 8 kPa between the stagnation pressure and the static pressure. Find the water velocity v at the tip.

p0 − p = 8 kPaρ = 1000 kg/m³
v = m/s
5.Hard
12d1​ = 100 mm, p1​ = 150 kPad2​ = 75 mm, p2​ = ?Δz = 3 m

Water flows up through a pipe that narrows from 100 mm to 75 mm while rising 3 m. At section 1 the pressure is 150 kPa and the velocity is 1.25 m/s. Ignoring losses, find the pressure p2 at section 2.

d1 = 100 mmd2 = 75 mmp1 = 150 kPav1 = 1.25 m/sΔz = 3 mρ = 1000 kg/m³
p2 = kPa
6.Hard
12d1​ = 75 mm, p1​ = 100 kPad2​ = 25 mm, p2​ = ?Δz = 3 m

Water flows up through a pipe that narrows from 75 mm to 25 mm while rising 3 m. At section 1 the pressure is 100 kPa and the velocity is 0.5 m/s. Ignoring losses, find the pressure p2 at section 2.

d1 = 75 mmd2 = 25 mmp1 = 100 kPav1 = 0.5 m/sΔz = 3 mρ = 1000 kg/m³
p2 = kPa

Answer key

  1. 1. d = 201.9 mm
  2. 2. d = 201.9 mm
  3. 3. v = 32.91 m/s
  4. 4. v = 4 m/s
  5. 5. p2 = 118.9 kPa
  6. 6. p2 = 60.57 kPa

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