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 = 40 mmh = 1.5 m

An open water tank drains through a round opening with a diameter of 40 mm in its side. The free surface is 1.5 m above the opening. Ignoring losses and the contraction of the jet, find the flow rate Q. Use g = 9.81 m/s².

h = 1.5 mg = 9.81 m/s²d = 40 mm
Q = L/s
2.Easy
12Q = 58 L/sv = 1.5 m/s, d = ?

A water line must carry 58 L/s. To limit noise and wear, the mean velocity should be 1.5 m/s. Find the inner pipe diameter d needed.

Q = 58 L/sv = 1.5 m/s
d = mm
3.Medium
12d1​ = 75 mm, p1​ = 280 kPad2​ = 25 mm, p2​ = ?

Water flows through a horizontal pipe that narrows from 75 mm to 25 mm. In the wide section the pressure is 280 kPa and the velocity is 1.5 m/s. Ignoring losses, find the pressure p2 in the narrow section.

d1 = 75 mmd2 = 25 mmp1 = 280 kPav1 = 1.5 m/sρ = 1000 kg/m³
p2 = kPa
4.Medium
12d1​ = 75 mm, p1​ = 190 kPad2​ = 40 mm, p2​ = ?

Water flows through a horizontal pipe that narrows from 75 mm to 40 mm. In the wide section the pressure is 190 kPa and the velocity is 3 m/s. Ignoring losses, find the pressure p2 in the narrow section.

d1 = 75 mmd2 = 40 mmp1 = 190 kPav1 = 3 m/sρ = 1000 kg/m³
p2 = kPa
5.Hard
d1​ = 300 mmd2​ = 150 mm12Δh = 300 mmmercuryQ = ?

A horizontal venturi meter (inlet 300 mm, throat 150 mm) carries water. A mercury U-tube manometer connected between the inlet and the throat shows a level difference of 300 mm. The discharge coefficient is 0.99. Find the flow rate Q. Use ρ = 1000 kg/m³ for water, 13 600 kg/m³ for mercury and g = 9.81 m/s².

d1 = 300 mmd2 = 150 mmΔh = 300 mmCd = 0.99ρHg = 13 600 kg/m³g = 9.81 m/s²
Q = L/s
6.Hard
12d1​ = 200 mm, p1​ = 200 kPad2​ = 100 mm, p2​ = ?Δz = 7 m

Water flows up through a pipe that narrows from 200 mm to 100 mm while rising 7 m. At section 1 the pressure is 200 kPa and the velocity is 1.75 m/s. Ignoring losses, find the pressure p2 at section 2.

d1 = 200 mmd2 = 100 mmp1 = 200 kPav1 = 1.75 m/sΔz = 7 mρ = 1000 kg/m³
p2 = kPa

Answer key

  1. 1. Q = 6.817 L/s
  2. 2. d = 221.9 mm
  3. 3. p2 = 190 kPa
  4. 4. p2 = 138.9 kPa
  5. 5. Q = 155.6 L/s
  6. 6. p2 = 108.4 kPa

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