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​ = 100 mm, v1​ = 2.5 m/sd2​ = 75 mm, v2​ = ?

Water flows through a pipe that narrows from 100 mm to 75 mm in diameter. The velocity in the wide section is 2.5 m/s. Find the velocity v2 in the narrow section.

d1 = 100 mmd2 = 75 mmv1 = 2.5 m/s
v2 = m/s
2.Easy
12d1​ = 75 mm, v1​ = 1.25 m/sd2​ = 50 mm

Water flows at 1.25 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 = 50 mmv1 = 1.25 m/s
Q = L/s
3.Medium
12d1​ = 150 mm, p1​ = ?d2​ = 75 mm, p2​ = 210 kPa

Water flows at 28 L/s through a horizontal pipe that narrows from 150 mm to 75 mm. The pressure in the narrow section is 210 kPa. Ignoring losses, find the pressure p1 in the wide section.

Q = 28 L/sd1 = 150 mmd2 = 75 mmp2 = 210 kPaρ = 1000 kg/m³
p1 = kPa
4.Medium
12d1​ = 150 mm, p1​ = ?d2​ = 75 mm, p2​ = 260 kPa

Water flows at 27 L/s through a horizontal pipe that narrows from 150 mm to 75 mm. The pressure in the narrow section is 260 kPa. Ignoring losses, find the pressure p1 in the wide section.

Q = 27 L/sd1 = 150 mmd2 = 75 mmp2 = 260 kPaρ = 1000 kg/m³
p1 = kPa
5.Hard
12d1​ = 100 mm, p1​ = 360 kPad2​ = 40 mm, p2​ = ?Δz = 4 m

Water flows up through a pipe that narrows from 100 mm to 40 mm while rising 4 m. At section 1 the pressure is 360 kPa and the velocity is 2 m/s. Ignoring losses, find the pressure p2 at section 2.

d1 = 100 mmd2 = 40 mmp1 = 360 kPav1 = 2 m/sΔz = 4 mρ = 1000 kg/m³
p2 = kPa
6.Hard
12d1​ = 75 mm, p1​ = 280 kPad2​ = 50 mm, p2​ = ?Δz = 2 m

Water flows up through a pipe that narrows from 75 mm to 50 mm while rising 2 m. At section 1 the pressure is 280 kPa and the velocity is 1.25 m/s. Ignoring losses, find the pressure p2 at section 2.

d1 = 75 mmd2 = 50 mmp1 = 280 kPav1 = 1.25 m/sΔz = 2 mρ = 1000 kg/m³
p2 = kPa

Answer key

  1. 1. v2 = 4.444 m/s
  2. 2. Q = 5.522 L/s
  3. 3. p1 = 228.8 kPa
  4. 4. p1 = 277.5 kPa
  5. 5. p2 = 244.6 kPa
  6. 6. p2 = 257.2 kPa

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