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
12d1​ = 100 mm, v1​ = 1.5 m/sd2​ = 50 mm, v2​ = ?

Water flows through a pipe that narrows from 100 mm to 50 mm in diameter. The velocity in the wide section is 1.5 m/s. Find the velocity v2 in the narrow section.

d1 = 100 mmd2 = 50 mmv1 = 1.5 m/s
v2 = m/s
2.Easy
12d1​ = 200 mm, v1​ = 1.75 m/sd2​ = 75 mm, v2​ = ?

Water flows through a pipe that narrows from 200 mm to 75 mm in diameter. The velocity in the wide section is 1.75 m/s. Find the velocity v2 in the narrow section.

d1 = 200 mmd2 = 75 mmv1 = 1.75 m/s
v2 = m/s
3.Medium
12d1​ = 75 mm, p1​ = 140 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 140 kPa and the velocity is 0.75 m/s. Ignoring losses, find the pressure p2 in the narrow section.

d1 = 75 mmd2 = 40 mmp1 = 140 kPav1 = 0.75 m/sρ = 1000 kg/m³
p2 = kPa
4.Medium
Q = ?d = 30 mm, Cd​ = 0.6h = 1 m

Water drains from a large open tank through a sharp-edged orifice with a diameter of 30 mm. The water level is kept 1 m above the orifice and the discharge coefficient is 0.6. Find the flow rate Q. Use g = 9.81 m/s².

d = 30 mmh = 1 mCd = 0.6g = 9.81 m/s²
Q = L/s
5.Hard
12d1​ = 100 mm, p1​ = 250 kPad2​ = 40 mm, p2​ = ?Δz = 4 m

Water flows up through a pipe that narrows from 100 mm to 40 mm while rising 4 m. At section 1 the pressure is 250 kPa and the velocity is 2 m/s. Ignoring losses, find the pressure p2 at section 2.

d1 = 100 mmd2 = 40 mmp1 = 250 kPav1 = 2 m/sΔz = 4 mρ = 1000 kg/m³
p2 = kPa
6.Hard
d1​ = 250 mmd2​ = 125 mm12Δh = 190 mmmercuryQ = ?

A horizontal venturi meter (inlet 250 mm, throat 125 mm) carries water. A mercury U-tube manometer connected between the inlet and the throat shows a level difference of 190 mm. The discharge coefficient is 0.95. 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 = 250 mmd2 = 125 mmΔh = 190 mmCd = 0.95ρHg = 13 600 kg/m³g = 9.81 m/s²
Q = L/s

Answer key

  1. 1. v2 = 6 m/s
  2. 2. v2 = 12.44 m/s
  3. 3. p2 = 136.8 kPa
  4. 4. Q = 1.879 L/s
  5. 5. p2 = 134.6 kPa
  6. 6. Q = 82.52 L/s

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