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​ = 1.75 m/sd2​ = 40 mm, v2​ = ?

Water flows through a pipe that narrows from 75 mm to 40 mm in diameter. The velocity in the wide section is 1.75 m/s. Find the velocity v2 in the narrow section.

d1 = 75 mmd2 = 40 mmv1 = 1.75 m/s
v2 = m/s
2.Easy
12d1​ = 100 mm, v1​ = 2 m/sd2​ = 50 mm, v2​ = ?

Water flows through a pipe that narrows from 100 mm to 50 mm in diameter. The velocity in the wide section is 2 m/s. Find the velocity v2 in the narrow section.

d1 = 100 mmd2 = 50 mmv1 = 2 m/s
v2 = m/s
3.Medium
12d1​ = 200 mm, p1​ = ?d2​ = 100 mm, p2​ = 220 kPa

Water flows at 36 L/s through a horizontal pipe that narrows from 200 mm to 100 mm. The pressure in the narrow section is 220 kPa. Ignoring losses, find the pressure p1 in the wide section.

Q = 36 L/sd1 = 200 mmd2 = 100 mmp2 = 220 kPaρ = 1000 kg/m³
p1 = kPa
4.Medium
12d1​ = 100 mm, p1​ = 130 kPad2​ = 50 mm, p2​ = ?

Water flows through a horizontal pipe that narrows from 100 mm to 50 mm. In the wide section the pressure is 130 kPa and the velocity is 2 m/s. Ignoring losses, find the pressure p2 in the narrow section.

d1 = 100 mmd2 = 50 mmp1 = 130 kPav1 = 2 m/sρ = 1000 kg/m³
p2 = kPa
5.Hard
12d1​ = 100 mm, p1​ = 110 kPad2​ = 40 mm, p2​ = ?Δz = 1 m

Water flows up through a pipe that narrows from 100 mm to 40 mm while rising 1 m. At section 1 the pressure is 110 kPa and the velocity is 1 m/s. Ignoring losses, find the pressure p2 at section 2.

d1 = 100 mmd2 = 40 mmp1 = 110 kPav1 = 1 m/sΔz = 1 mρ = 1000 kg/m³
p2 = kPa
6.Hard
pair​ = 190 kPav = ?d = 30 mmh = 3.5 m

A closed water tank has compressed air above the water at a gauge pressure of 190 kPa. Water leaves through an opening with a diameter of 30 mm, 3.5 m below the water surface, into the open air. Ignoring losses, find the jet velocity v. Use g = 9.81 m/s².

pair = 190 kPa (gauge)h = 3.5 md = 30 mmρ = 1000 kg/m³g = 9.81 m/s²
v = m/s

Answer key

  1. 1. v2 = 6.152 m/s
  2. 2. v2 = 8 m/s
  3. 3. p1 = 229.8 kPa
  4. 4. p2 = 100 kPa
  5. 5. p2 = 81.16 kPa
  6. 6. v = 21.18 m/s

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