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​ = 200 mm, v1​ = 0.5 m/sd2​ = 100 mm

Water flows at 0.5 m/s through the wide section of the pipe, which has a diameter of 200 mm. Find the volume flow rate Q.

d1 = 200 mmd2 = 100 mmv1 = 0.5 m/s
Q = L/s
2.Easy
12d1​ = 75 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 75 mm. Find the volume flow rate Q.

d1 = 75 mmd2 = 40 mmv1 = 1 m/s
Q = L/s
3.Medium
12d1​ = 150 mm, p1​ = 390 kPad2​ = 100 mm, p2​ = ?

Water flows through a horizontal pipe that narrows from 150 mm to 100 mm. In the wide section the pressure is 390 kPa and the velocity is 2.5 m/s. Ignoring losses, find the pressure p2 in the narrow section.

d1 = 150 mmd2 = 100 mmp1 = 390 kPav1 = 2.5 m/sρ = 1000 kg/m³
p2 = kPa
4.Medium
12d1​ = 150 mm, p1​ = ?d2​ = 100 mm, p2​ = 70 kPa

Water flows at 24 L/s through a horizontal pipe that narrows from 150 mm to 100 mm. The pressure in the narrow section is 70 kPa. Ignoring losses, find the pressure p1 in the wide section.

Q = 24 L/sd1 = 150 mmd2 = 100 mmp2 = 70 kPaρ = 1000 kg/m³
p1 = kPa
5.Hard
12d1​ = 100 mm, p1​ = 260 kPad2​ = 75 mm, p2​ = ?Δz = 2 m

Water flows up through a pipe that narrows from 100 mm to 75 mm while rising 2 m. At section 1 the pressure is 260 kPa and the velocity is 1 m/s. Ignoring losses, find the pressure p2 at section 2.

d1 = 100 mmd2 = 75 mmp1 = 260 kPav1 = 1 m/sΔz = 2 mρ = 1000 kg/m³
p2 = kPa
6.Hard
pair​ = 50 kPav = ?d = 20 mmh = 5 m

A closed water tank has compressed air above the water at a gauge pressure of 50 kPa. Water leaves through an opening with a diameter of 20 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 = 50 kPa (gauge)h = 5 md = 20 mmρ = 1000 kg/m³g = 9.81 m/s²
v = m/s

Answer key

  1. 1. Q = 15.71 L/s
  2. 2. Q = 4.418 L/s
  3. 3. p2 = 377.3 kPa
  4. 4. p1 = 73.75 kPa
  5. 5. p2 = 239.3 kPa
  6. 6. v = 14.07 m/s

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