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 = 29 L/sv = 3 m/s, d = ?

A water line must carry 29 L/s. To limit noise and wear, the mean velocity should be 3 m/s. Find the inner pipe diameter d needed.

Q = 29 L/sv = 3 m/s
d = mm
2.Easy
12d1​ = 100 mm, v1​ = 1 m/sd2​ = 40 mm

Water flows at 1 m/s through the wide section of the pipe, which has a diameter of 100 mm. Find the volume flow rate Q.

d1 = 100 mmd2 = 40 mmv1 = 1 m/s
Q = L/s
3.Medium
v = ?p0​pp0​ − p = 1050 Pastagnation point

A pitot-static tube in a wind tunnel reads a difference of 1050 Pa between the stagnation pressure and the static pressure. The air density is 1.2 kg/m³. Find the air speed v.

p0 − p = 1050 Paρ = 1.2 kg/m³
v = m/s
4.Medium
v = ?p0​pp0​ − p = 350 Pastagnation point

A pitot-static tube in a wind tunnel reads a difference of 350 Pa between the stagnation pressure and the static pressure. The air density is 1.2 kg/m³. Find the air speed v.

p0 − p = 350 Paρ = 1.2 kg/m³
v = m/s
5.Hard
12d1​ = 100 mm, p1​ = 210 kPad2​ = 75 mm, p2​ = ?Δz = 9 m

Water flows up through a pipe that narrows from 100 mm to 75 mm while rising 9 m. At section 1 the pressure is 210 kPa and the velocity is 2.75 m/s. Ignoring losses, find the pressure p2 at section 2.

d1 = 100 mmd2 = 75 mmp1 = 210 kPav1 = 2.75 m/sΔz = 9 mρ = 1000 kg/m³
p2 = kPa
6.Hard
12d1​ = 100 mm, p1​ = 100 kPad2​ = 75 mm, p2​ = ?Δz = 5 m

Water flows up through a pipe that narrows from 100 mm to 75 mm while rising 5 m. At section 1 the pressure is 100 kPa and the velocity is 0.75 m/s. Ignoring losses, find the pressure p2 at section 2.

d1 = 100 mmd2 = 75 mmp1 = 100 kPav1 = 0.75 m/sΔz = 5 mρ = 1000 kg/m³
p2 = kPa

Answer key

  1. 1. d = 110.9 mm
  2. 2. Q = 7.854 L/s
  3. 3. v = 41.83 m/s
  4. 4. v = 24.15 m/s
  5. 5. p2 = 113.5 kPa
  6. 6. p2 = 50.34 kPa

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