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
12Q = 17 L/sv = 2.5 m/s, d = ?

A water line must carry 17 L/s. To limit noise and wear, the mean velocity should be 2.5 m/s. Find the inner pipe diameter d needed.

Q = 17 L/sv = 2.5 m/s
d = mm
2.Easy
12Q = 22 L/sv = 2.5 m/s, d = ?

A water line must carry 22 L/s. To limit noise and wear, the mean velocity should be 2.5 m/s. Find the inner pipe diameter d needed.

Q = 22 L/sv = 2.5 m/s
d = mm
3.Medium
12d1​ = 150 mm, p1​ = ?d2​ = 75 mm, p2​ = 250 kPa

Water flows at 32 L/s through a horizontal pipe that narrows from 150 mm to 75 mm. The pressure in the narrow section is 250 kPa. Ignoring losses, find the pressure p1 in the wide section.

Q = 32 L/sd1 = 150 mmd2 = 75 mmp2 = 250 kPaρ = 1000 kg/m³
p1 = kPa
4.Medium
d1​ = 100 mmd2​ = 50 mm12p1​ − p2​ = 38 kPaQ = ?

Water flows through a horizontal venturi meter with an inlet diameter of 100 mm and a throat diameter of 50 mm. The pressure at the inlet is 38 kPa higher than at the throat. Ignoring losses, find the flow rate Q.

d1 = 100 mmd2 = 50 mmp1 − p2 = 38 kPaρ = 1000 kg/m³
Q = L/s
5.Hard
12d1​ = 100 mm, p1​ = 160 kPad2​ = 75 mm, p2​ = ?Δz = 6 m

Water flows up through a pipe that narrows from 100 mm to 75 mm while rising 6 m. At section 1 the pressure is 160 kPa and the velocity is 1.75 m/s. Ignoring losses, find the pressure p2 at section 2.

d1 = 100 mmd2 = 75 mmp1 = 160 kPav1 = 1.75 m/sΔz = 6 mρ = 1000 kg/m³
p2 = kPa
6.Hard
d1​ = 100 mmd2​ = 60 mm12Δh = 110 mmmercuryQ = ?

A horizontal venturi meter (inlet 100 mm, throat 60 mm) carries water. A mercury U-tube manometer connected between the inlet and the throat shows a level difference of 110 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 = 100 mmd2 = 60 mmΔh = 110 mmCd = 0.99ρHg = 13 600 kg/m³g = 9.81 m/s²
Q = L/s

Answer key

  1. 1. d = 93.05 mm
  2. 2. d = 105.9 mm
  3. 3. p1 = 274.6 kPa
  4. 4. Q = 17.68 L/s
  5. 5. p2 = 97.83 kPa
  6. 6. Q = 15.65 L/s

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