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​ = 75 mm, v1​ = 0.5 m/sd2​ = 50 mm, v2​ = ?

Water flows through a pipe that narrows from 75 mm to 50 mm in diameter. The velocity in the wide section is 0.5 m/s. Find the velocity v2 in the narrow section.

d1 = 75 mmd2 = 50 mmv1 = 0.5 m/s
v2 = m/s
2.Easy
12d1​ = 150 mm, v1​ = 0.5 m/sd2​ = 40 mm

Water flows at 0.5 m/s through the wide section of the pipe, which has a diameter of 150 mm. Find the volume flow rate Q.

d1 = 150 mmd2 = 40 mmv1 = 0.5 m/s
Q = L/s
3.Medium
12d1​ = 200 mm, p1​ = 120 kPad2​ = 75 mm, p2​ = ?

Water flows through a horizontal pipe that narrows from 200 mm to 75 mm. In the wide section the pressure is 120 kPa and the velocity is 0.5 m/s. Ignoring losses, find the pressure p2 in the narrow section.

d1 = 200 mmd2 = 75 mmp1 = 120 kPav1 = 0.5 m/sρ = 1000 kg/m³
p2 = kPa
4.Medium
v = ?p0​pp0​ − p = 950 Pastagnation point

A pitot-static tube in a wind tunnel reads a difference of 950 Pa between the stagnation pressure and the static pressure. The air density is 1.2 kg/m³. Find the air speed v.

p0 − p = 950 Paρ = 1.2 kg/m³
v = m/s
5.Hard
12d1​ = 150 mm, p1​ = 350 kPad2​ = 50 mm, p2​ = ?Δz = 7 m

Water flows up through a pipe that narrows from 150 mm to 50 mm while rising 7 m. At section 1 the pressure is 350 kPa and the velocity is 1.5 m/s. Ignoring losses, find the pressure p2 at section 2.

d1 = 150 mmd2 = 50 mmp1 = 350 kPav1 = 1.5 m/sΔz = 7 mρ = 1000 kg/m³
p2 = kPa
6.Hard
12d1​ = 75 mm, p1​ = 240 kPad2​ = 50 mm, p2​ = ?Δz = 5 m

Water flows up through a pipe that narrows from 75 mm to 50 mm while rising 5 m. At section 1 the pressure is 240 kPa and the velocity is 2.5 m/s. Ignoring losses, find the pressure p2 at section 2.

d1 = 75 mmd2 = 50 mmp1 = 240 kPav1 = 2.5 m/sΔz = 5 mρ = 1000 kg/m³
p2 = kPa

Answer key

  1. 1. v2 = 1.125 m/s
  2. 2. Q = 8.836 L/s
  3. 3. p2 = 113.8 kPa
  4. 4. v = 39.79 m/s
  5. 5. p2 = 191.3 kPa
  6. 6. p2 = 178.3 kPa

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