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 = 58 L/sv = 1.5 m/s, d = ?

A water line must carry 58 L/s. To limit noise and wear, the mean velocity should be 1.5 m/s. Find the inner pipe diameter d needed.

Q = 58 L/sv = 1.5 m/s
d = mm
2.Easy
12Q = 53 L/sv = 3 m/s, d = ?

A water line must carry 53 L/s. To limit noise and wear, the mean velocity should be 3 m/s. Find the inner pipe diameter d needed.

Q = 53 L/sv = 3 m/s
d = mm
3.Medium
12d1​ = 100 mm, p1​ = 390 kPad2​ = 40 mm, p2​ = ?

Water flows through a horizontal pipe that narrows from 100 mm to 40 mm. In the wide section the pressure is 390 kPa and the velocity is 2.25 m/s. Ignoring losses, find the pressure p2 in the narrow section.

d1 = 100 mmd2 = 40 mmp1 = 390 kPav1 = 2.25 m/sρ = 1000 kg/m³
p2 = kPa
4.Medium
12d1​ = 100 mm, p1​ = 400 kPad2​ = 40 mm, p2​ = ?

Water flows through a horizontal pipe that narrows from 100 mm to 40 mm. In the wide section the pressure is 400 kPa and the velocity is 0.75 m/s. Ignoring losses, find the pressure p2 in the narrow section.

d1 = 100 mmd2 = 40 mmp1 = 400 kPav1 = 0.75 m/sρ = 1000 kg/m³
p2 = kPa
5.Hard
pair​ = 80 kPav = ?d = 40 mmh = 3 m

A closed water tank has compressed air above the water at a gauge pressure of 80 kPa. Water leaves through an opening with a diameter of 40 mm, 3 m below the water surface, into the open air. Ignoring losses, find the jet velocity v. Use g = 9.81 m/s².

pair = 80 kPa (gauge)h = 3 md = 40 mmρ = 1000 kg/m³g = 9.81 m/s²
v = m/s
6.Hard
pair​ = 200 kPav = ?d = 50 mmh = 5 m

A closed water tank has compressed air above the water at a gauge pressure of 200 kPa. Water leaves through an opening with a diameter of 50 mm, 5 m below the water surface, into the open air. Ignoring losses, find the jet velocity v. Use g = 9.81 m/s².

pair = 200 kPa (gauge)h = 5 md = 50 mmρ = 1000 kg/m³g = 9.81 m/s²
v = m/s

Answer key

  1. 1. d = 221.9 mm
  2. 2. d = 150 mm
  3. 3. p2 = 293.7 kPa
  4. 4. p2 = 389.3 kPa
  5. 5. v = 14.79 m/s
  6. 6. v = 22.32 m/s

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