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​ = 2 m/sd2​ = 100 mm, v2​ = ?

Water flows through a pipe that narrows from 200 mm to 100 mm in diameter. The velocity in the wide section is 2 m/s. Find the velocity v2 in the narrow section.

d1 = 200 mmd2 = 100 mmv1 = 2 m/s
v2 = m/s
2.Easy
12d1​ = 100 mm, v1​ = 1 m/sd2​ = 75 mm

Water flows at 1 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 m/s
Q = L/s
3.Medium
12d1​ = 100 mm, p1​ = 380 kPad2​ = 40 mm, p2​ = ?

Water flows through a horizontal pipe that narrows from 100 mm to 40 mm. In the wide section the pressure is 380 kPa and the velocity is 2.25 m/s. Ignoring losses, find the pressure p2 in the narrow section.

d1 = 100 mmd2 = 40 mmp1 = 380 kPav1 = 2.25 m/sρ = 1000 kg/m³
p2 = kPa
4.Medium
d1​ = 300 mmd2​ = 150 mm12p1​ − p2​ = 51 kPaQ = ?

Water flows through a horizontal venturi meter with an inlet diameter of 300 mm and a throat diameter of 150 mm. The pressure at the inlet is 51 kPa higher than at the throat. Ignoring losses, find the flow rate Q.

d1 = 300 mmd2 = 150 mmp1 − p2 = 51 kPaρ = 1000 kg/m³
Q = L/s
5.Hard
12d1​ = 75 mm, p1​ = 390 kPad2​ = 40 mm, p2​ = ?Δz = 5 m

Water flows up through a pipe that narrows from 75 mm to 40 mm while rising 5 m. At section 1 the pressure is 390 kPa and the velocity is 0.5 m/s. Ignoring losses, find the pressure p2 at section 2.

d1 = 75 mmd2 = 40 mmp1 = 390 kPav1 = 0.5 m/sΔz = 5 mρ = 1000 kg/m³
p2 = kPa
6.Hard
12d1​ = 75 mm, p1​ = 150 kPad2​ = 25 mm, p2​ = ?Δz = 4 m

Water flows up through a pipe that narrows from 75 mm to 25 mm while rising 4 m. At section 1 the pressure is 150 kPa and the velocity is 1.25 m/s. Ignoring losses, find the pressure p2 at section 2.

d1 = 75 mmd2 = 25 mmp1 = 150 kPav1 = 1.25 m/sΔz = 4 mρ = 1000 kg/m³
p2 = kPa

Answer key

  1. 1. v2 = 8 m/s
  2. 2. Q = 7.854 L/s
  3. 3. p2 = 283.7 kPa
  4. 4. Q = 184.3 L/s
  5. 5. p2 = 339.5 kPa
  6. 6. p2 = 48.26 kPa

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