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​ = 75 mm, v1​ = 0.75 m/sd2​ = 25 mm

Water flows at 0.75 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 = 25 mmv1 = 0.75 m/s
Q = L/s
2.Easy
12d1​ = 75 mm, v1​ = 2.25 m/sd2​ = 50 mm, v2​ = ?

Water flows through a pipe that narrows from 75 mm to 50 mm in diameter. The velocity in the wide section is 2.25 m/s. Find the velocity v2 in the narrow section.

d1 = 75 mmd2 = 50 mmv1 = 2.25 m/s
v2 = m/s
3.Medium
d1​ = 80 mmd2​ = 40 mm12p1​ − p2​ = 31 kPaQ = ?

Water flows through a horizontal venturi meter with an inlet diameter of 80 mm and a throat diameter of 40 mm. The pressure at the inlet is 31 kPa higher than at the throat. Ignoring losses, find the flow rate Q.

d1 = 80 mmd2 = 40 mmp1 − p2 = 31 kPaρ = 1000 kg/m³
Q = L/s
4.Medium
d1​ = 200 mmd2​ = 100 mm12p1​ − p2​ = 32 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 32 kPa higher than at the throat. Ignoring losses, find the flow rate Q.

d1 = 200 mmd2 = 100 mmp1 − p2 = 32 kPaρ = 1000 kg/m³
Q = L/s
5.Hard
12d1​ = 100 mm, p1​ = 270 kPad2​ = 40 mm, p2​ = ?Δz = 7 m

Water flows up through a pipe that narrows from 100 mm to 40 mm while rising 7 m. At section 1 the pressure is 270 kPa and the velocity is 2 m/s. Ignoring losses, find the pressure p2 at section 2.

d1 = 100 mmd2 = 40 mmp1 = 270 kPav1 = 2 m/sΔz = 7 mρ = 1000 kg/m³
p2 = kPa
6.Hard
12d1​ = 100 mm, p1​ = 150 kPad2​ = 75 mm, p2​ = ?Δz = 7 m

Water flows up through a pipe that narrows from 100 mm to 75 mm while rising 7 m. At section 1 the pressure is 150 kPa and the velocity is 2 m/s. Ignoring losses, find the pressure p2 at section 2.

d1 = 100 mmd2 = 75 mmp1 = 150 kPav1 = 2 m/sΔz = 7 mρ = 1000 kg/m³
p2 = kPa

Answer key

  1. 1. Q = 3.313 L/s
  2. 2. v2 = 5.063 m/s
  3. 3. Q = 10.22 L/s
  4. 4. Q = 64.89 L/s
  5. 5. p2 = 125.2 kPa
  6. 6. p2 = 77.01 kPa

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