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​ = 75 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 = 75 mmv1 = 0.5 m/s
Q = L/s
2.Easy
12d1​ = 75 mm, v1​ = 1.5 m/sd2​ = 25 mm, v2​ = ?

Water flows through a pipe that narrows from 75 mm to 25 mm in diameter. The velocity in the wide section is 1.5 m/s. Find the velocity v2 in the narrow section.

d1 = 75 mmd2 = 25 mmv1 = 1.5 m/s
v2 = m/s
3.Medium
12d1​ = 200 mm, p1​ = ?d2​ = 100 mm, p2​ = 240 kPa

Water flows at 30 L/s through a horizontal pipe that narrows from 200 mm to 100 mm. The pressure in the narrow section is 240 kPa. Ignoring losses, find the pressure p1 in the wide section.

Q = 30 L/sd1 = 200 mmd2 = 100 mmp2 = 240 kPaρ = 1000 kg/m³
p1 = kPa
4.Medium
12d1​ = 200 mm, p1​ = 290 kPad2​ = 75 mm, p2​ = ?

Water flows through a horizontal pipe that narrows from 200 mm to 75 mm. In the wide section the pressure is 290 kPa and the velocity is 0.75 m/s. Ignoring losses, find the pressure p2 in the narrow section.

d1 = 200 mmd2 = 75 mmp1 = 290 kPav1 = 0.75 m/sρ = 1000 kg/m³
p2 = kPa
5.Hard
12d1​ = 75 mm, p1​ = 160 kPad2​ = 25 mm, p2​ = ?Δz = 6 m

Water flows up through a pipe that narrows from 75 mm to 25 mm while rising 6 m. At section 1 the pressure is 160 kPa and the velocity is 1.25 m/s. Ignoring losses, find the pressure p2 at section 2.

d1 = 75 mmd2 = 25 mmp1 = 160 kPav1 = 1.25 m/sΔz = 6 mρ = 1000 kg/m³
p2 = kPa
6.Hard
12d1​ = 100 mm, p1​ = 330 kPad2​ = 75 mm, p2​ = ?Δz = 8 m

Water flows up through a pipe that narrows from 100 mm to 75 mm while rising 8 m. At section 1 the pressure is 330 kPa and the velocity is 3 m/s. Ignoring losses, find the pressure p2 at section 2.

d1 = 100 mmd2 = 75 mmp1 = 330 kPav1 = 3 m/sΔz = 8 mρ = 1000 kg/m³
p2 = kPa

Answer key

  1. 1. Q = 15.71 L/s
  2. 2. v2 = 13.5 m/s
  3. 3. p1 = 246.8 kPa
  4. 4. p2 = 276.1 kPa
  5. 5. p2 = 38.64 kPa
  6. 6. p2 = 241.8 kPa

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