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.

New worksheetPractise online with hints

For teachers: free to print, copy and use in class. Every new worksheet has new values and its own answer key. A link to ExamProblems on your course page is appreciated.

Name: ____________________   Date: ____________

1.Easy
vd = 10 mmh = 7.5 m

An open water tank drains through a round opening with a diameter of 10 mm in its side. The free surface is 7.5 m above the opening. Ignoring losses and the contraction of the jet, find the flow rate Q. Use g = 9.81 m/s².

h = 7.5 mg = 9.81 m/s²d = 10 mm
Q = L/s
2.Easy
12Q = 33 L/sv = 2 m/s, d = ?

A water line must carry 33 L/s. To limit noise and wear, the mean velocity should be 2 m/s. Find the inner pipe diameter d needed.

Q = 33 L/sv = 2 m/s
d = mm
3.Medium
12d1​ = 150 mm, p1​ = 240 kPad2​ = 50 mm, p2​ = ?

Water flows through a horizontal pipe that narrows from 150 mm to 50 mm. In the wide section the pressure is 240 kPa and the velocity is 1 m/s. Ignoring losses, find the pressure p2 in the narrow section.

d1 = 150 mmd2 = 50 mmp1 = 240 kPav1 = 1 m/sρ = 1000 kg/m³
p2 = kPa
4.Medium
d1​ = 200 mmd2​ = 100 mm12p1​ − p2​ = 58 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 58 kPa higher than at the throat. Ignoring losses, find the flow rate Q.

d1 = 200 mmd2 = 100 mmp1 − p2 = 58 kPaρ = 1000 kg/m³
Q = L/s
5.Hard
12d1​ = 100 mm, p1​ = 200 kPad2​ = 50 mm, p2​ = ?Δz = 6 m

Water flows up through a pipe that narrows from 100 mm to 50 mm while rising 6 m. At section 1 the pressure is 200 kPa and the velocity is 0.75 m/s. Ignoring losses, find the pressure p2 at section 2.

d1 = 100 mmd2 = 50 mmp1 = 200 kPav1 = 0.75 m/sΔz = 6 mρ = 1000 kg/m³
p2 = kPa
6.Hard
12d1​ = 100 mm, p1​ = 300 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 300 kPa and the velocity is 2.75 m/s. Ignoring losses, find the pressure p2 at section 2.

d1 = 100 mmd2 = 75 mmp1 = 300 kPav1 = 2.75 m/sΔz = 5 mρ = 1000 kg/m³
p2 = kPa

Answer key

  1. 1. Q = 0.9527 L/s
  2. 2. d = 144.9 mm
  3. 3. p2 = 200 kPa
  4. 4. Q = 87.36 L/s
  5. 5. p2 = 136.9 kPa
  6. 6. p2 = 242.8 kPa

Full step-by-step solutions: practise this topic on examproblems.com.