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​ = 150 mm, v1​ = 1 m/sd2​ = 100 mm, v2​ = ?

Water flows through a pipe that narrows from 150 mm to 100 mm in diameter. The velocity in the wide section is 1 m/s. Find the velocity v2 in the narrow section.

d1 = 150 mmd2 = 100 mmv1 = 1 m/s
v2 = m/s
2.Easy
12d1​ = 200 mm, v1​ = 0.5 m/sd2​ = 50 mm, v2​ = ?

Water flows through a pipe that narrows from 200 mm to 50 mm in diameter. The velocity in the wide section is 0.5 m/s. Find the velocity v2 in the narrow section.

d1 = 200 mmd2 = 50 mmv1 = 0.5 m/s
v2 = m/s
3.Medium
Q = ?d = 50 mm, Cd​ = 0.61h = 4 m

Water drains from a large open tank through a sharp-edged orifice with a diameter of 50 mm. The water level is kept 4 m above the orifice and the discharge coefficient is 0.61. Find the flow rate Q. Use g = 9.81 m/s².

d = 50 mmh = 4 mCd = 0.61g = 9.81 m/s²
Q = L/s
4.Medium
12d1​ = 200 mm, p1​ = 220 kPad2​ = 75 mm, p2​ = ?

Water flows through a horizontal pipe that narrows from 200 mm to 75 mm. In the wide section the pressure is 220 kPa and the velocity is 0.75 m/s. Ignoring losses, find the pressure p2 in the narrow section.

d1 = 200 mmd2 = 75 mmp1 = 220 kPav1 = 0.75 m/sρ = 1000 kg/m³
p2 = kPa
5.Hard
d1​ = 200 mmd2​ = 150 mm12Δh = 240 mmmercuryQ = ?

A horizontal venturi meter (inlet 200 mm, throat 150 mm) carries water. A mercury U-tube manometer connected between the inlet and the throat shows a level difference of 240 mm. The discharge coefficient is 0.97. 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 = 200 mmd2 = 150 mmΔh = 240 mmCd = 0.97ρHg = 13 600 kg/m³g = 9.81 m/s²
Q = L/s
6.Hard
12d1​ = 100 mm, p1​ = 180 kPad2​ = 25 mm, p2​ = ?Δz = 2 m

Water flows up through a pipe that narrows from 100 mm to 25 mm while rising 2 m. At section 1 the pressure is 180 kPa and the velocity is 0.75 m/s. Ignoring losses, find the pressure p2 at section 2.

d1 = 100 mmd2 = 25 mmp1 = 180 kPav1 = 0.75 m/sΔz = 2 mρ = 1000 kg/m³
p2 = kPa

Answer key

  1. 1. v2 = 2.25 m/s
  2. 2. v2 = 8 m/s
  3. 3. Q = 10.61 L/s
  4. 4. p2 = 206.1 kPa
  5. 5. Q = 159.7 L/s
  6. 6. p2 = 88.66 kPa

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