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​ = 150 mm, v1​ = 1 m/sd2​ = 100 mm, v2​ = ?

Water flows through a pipe that narrows from 150 mm to 100 mm in diameter. The velocity in the wide section is 1 m/s. Find the velocity v2 in the narrow section.

d1 = 150 mmd2 = 100 mmv1 = 1 m/s
v2 = m/s
2.Easy
12d1​ = 100 mm, v1​ = 1.25 m/sd2​ = 75 mm

Water flows at 1.25 m/s through the wide section of the pipe, which has a diameter of 100 mm. Find the volume flow rate Q.

d1 = 100 mmd2 = 75 mmv1 = 1.25 m/s
Q = L/s
3.Medium
12d1​ = 100 mm, p1​ = ?d2​ = 75 mm, p2​ = 180 kPa

Water flows at 10 L/s through a horizontal pipe that narrows from 100 mm to 75 mm. The pressure in the narrow section is 180 kPa. Ignoring losses, find the pressure p1 in the wide section.

Q = 10 L/sd1 = 100 mmd2 = 75 mmp2 = 180 kPaρ = 1000 kg/m³
p1 = kPa
4.Medium
d1​ = 200 mmd2​ = 100 mm12p1​ − p2​ = 23 kPaQ = ?

Water flows through a horizontal venturi meter with an inlet diameter of 200 mm and a throat diameter of 100 mm. The pressure at the inlet is 23 kPa higher than at the throat. Ignoring losses, find the flow rate Q.

d1 = 200 mmd2 = 100 mmp1 − p2 = 23 kPaρ = 1000 kg/m³
Q = L/s
5.Hard
12d1​ = 100 mm, p1​ = 300 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 300 kPa and the velocity is 0.75 m/s. Ignoring losses, find the pressure p2 at section 2.

d1 = 100 mmd2 = 40 mmp1 = 300 kPav1 = 0.75 m/sΔz = 1 mρ = 1000 kg/m³
p2 = kPa
6.Hard
12d1​ = 100 mm, p1​ = 210 kPad2​ = 75 mm, p2​ = ?Δz = 5 m

Water flows up through a pipe that narrows from 100 mm to 75 mm while rising 5 m. At section 1 the pressure is 210 kPa and the velocity is 2.5 m/s. Ignoring losses, find the pressure p2 at section 2.

d1 = 100 mmd2 = 75 mmp1 = 210 kPav1 = 2.5 m/sΔz = 5 mρ = 1000 kg/m³
p2 = kPa

Answer key

  1. 1. v2 = 2.25 m/s
  2. 2. Q = 9.817 L/s
  3. 3. p1 = 181.8 kPa
  4. 4. Q = 55.02 L/s
  5. 5. p2 = 279.5 kPa
  6. 6. p2 = 154.2 kPa

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