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 = 21 L/sv = 1.5 m/s, d = ?

A water line must carry 21 L/s. To limit noise and wear, the mean velocity should be 1.5 m/s. Find the inner pipe diameter d needed.

Q = 21 L/sv = 1.5 m/s
d = mm
2.Easy
12Q = 8 L/sv = 2.5 m/s, d = ?

A water line must carry 8 L/s. To limit noise and wear, the mean velocity should be 2.5 m/s. Find the inner pipe diameter d needed.

Q = 8 L/sv = 2.5 m/s
d = mm
3.Medium
12d1​ = 150 mm, p1​ = ?d2​ = 75 mm, p2​ = 70 kPa

Water flows at 20 L/s through a horizontal pipe that narrows from 150 mm to 75 mm. The pressure in the narrow section is 70 kPa. Ignoring losses, find the pressure p1 in the wide section.

Q = 20 L/sd1 = 150 mmd2 = 75 mmp2 = 70 kPaρ = 1000 kg/m³
p1 = kPa
4.Medium
12d1​ = 100 mm, p1​ = 240 kPad2​ = 75 mm, p2​ = ?

Water flows through a horizontal pipe that narrows from 100 mm to 75 mm. In the wide section the pressure is 240 kPa and the velocity is 1.75 m/s. Ignoring losses, find the pressure p2 in the narrow section.

d1 = 100 mmd2 = 75 mmp1 = 240 kPav1 = 1.75 m/sρ = 1000 kg/m³
p2 = kPa
5.Hard
12d1​ = 75 mm, p1​ = 140 kPad2​ = 50 mm, p2​ = ?Δz = 3 m

Water flows up through a pipe that narrows from 75 mm to 50 mm while rising 3 m. At section 1 the pressure is 140 kPa and the velocity is 0.75 m/s. Ignoring losses, find the pressure p2 at section 2.

d1 = 75 mmd2 = 50 mmp1 = 140 kPav1 = 0.75 m/sΔz = 3 mρ = 1000 kg/m³
p2 = kPa
6.Hard
H = ?d1​ = 100 mmp1​ = 140 kPad2​ = 20 mm

A fountain nozzle points straight up. Just below the nozzle the supply pipe has a diameter of 100 mm and a gauge pressure of 140 kPa. The nozzle exit diameter is 20 mm, and the height difference across the nozzle is negligible. Ignoring losses and air resistance, find the height H the jet rises above the nozzle. Use g = 9.81 m/s².

d1 = 100 mmp1 = 140 kPa (gauge)d2 = 20 mmρ = 1000 kg/m³g = 9.81 m/s²
H = m

Answer key

  1. 1. d = 133.5 mm
  2. 2. d = 63.83 mm
  3. 3. p1 = 79.61 kPa
  4. 4. p2 = 236.7 kPa
  5. 5. p2 = 109.4 kPa
  6. 6. H = 14.29 m

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