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​ = 150 mm, v1​ = 0.75 m/sd2​ = 50 mm, v2​ = ?

Water flows through a pipe that narrows from 150 mm to 50 mm in diameter. The velocity in the wide section is 0.75 m/s. Find the velocity v2 in the narrow section.

d1 = 150 mmd2 = 50 mmv1 = 0.75 m/s
v2 = m/s
2.Easy
12Q = 45 L/sv = 3 m/s, d = ?

A water line must carry 45 L/s. To limit noise and wear, the mean velocity should be 3 m/s. Find the inner pipe diameter d needed.

Q = 45 L/sv = 3 m/s
d = mm
3.Medium
12d1​ = 75 mm, p1​ = 120 kPad2​ = 50 mm, p2​ = ?

Water flows through a horizontal pipe that narrows from 75 mm to 50 mm. In the wide section the pressure is 120 kPa and the velocity is 2 m/s. Ignoring losses, find the pressure p2 in the narrow section.

d1 = 75 mmd2 = 50 mmp1 = 120 kPav1 = 2 m/sρ = 1000 kg/m³
p2 = kPa
4.Medium
v = ?p0​pp0​ − p = 9 kPastagnation point

A pitot-static tube in a water pipe reads a difference of 9 kPa between the stagnation pressure and the static pressure. Find the water velocity v at the tip.

p0 − p = 9 kPaρ = 1000 kg/m³
v = m/s
5.Hard
12d1​ = 75 mm, p1​ = 220 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 220 kPa and the velocity is 2.5 m/s. Ignoring losses, find the pressure p2 at section 2.

d1 = 75 mmd2 = 50 mmp1 = 220 kPav1 = 2.5 m/sΔz = 5 mρ = 1000 kg/m³
p2 = kPa
6.Hard
12d1​ = 100 mm, p1​ = 360 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 360 kPa and the velocity is 1.75 m/s. Ignoring losses, find the pressure p2 at section 2.

d1 = 100 mmd2 = 75 mmp1 = 360 kPav1 = 1.75 m/sΔz = 5 mρ = 1000 kg/m³
p2 = kPa

Answer key

  1. 1. v2 = 6.75 m/s
  2. 2. d = 138.2 mm
  3. 3. p2 = 111.9 kPa
  4. 4. v = 4.243 m/s
  5. 5. p2 = 158.3 kPa
  6. 6. p2 = 307.6 kPa

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