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
v = ?h = 1.5 m

An open water tank drains through a small opening in its side. The free surface is 1.5 m above the opening. Ignoring losses, find the jet velocity v at the opening. Use g = 9.81 m/s².

h = 1.5 mg = 9.81 m/s²
v = m/s
2.Easy
12Q = 29 L/sv = 2.5 m/s, d = ?

A water line must carry 29 L/s. To limit noise and wear, the mean velocity should be 2.5 m/s. Find the inner pipe diameter d needed.

Q = 29 L/sv = 2.5 m/s
d = mm
3.Medium
12d1​ = 75 mm, p1​ = 260 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 260 kPa and the velocity is 0.5 m/s. Ignoring losses, find the pressure p2 in the narrow section.

d1 = 75 mmd2 = 40 mmp1 = 260 kPav1 = 0.5 m/sρ = 1000 kg/m³
p2 = kPa
4.Medium
12d1​ = 150 mm, p1​ = 280 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 280 kPa and the velocity is 1.25 m/s. Ignoring losses, find the pressure p2 in the narrow section.

d1 = 150 mmd2 = 50 mmp1 = 280 kPav1 = 1.25 m/sρ = 1000 kg/m³
p2 = kPa
5.Hard
12d1​ = 200 mm, p1​ = 350 kPad2​ = 100 mm, p2​ = ?Δz = 3 m

Water flows up through a pipe that narrows from 200 mm to 100 mm while rising 3 m. At section 1 the pressure is 350 kPa and the velocity is 2.25 m/s. Ignoring losses, find the pressure p2 at section 2.

d1 = 200 mmd2 = 100 mmp1 = 350 kPav1 = 2.25 m/sΔz = 3 mρ = 1000 kg/m³
p2 = kPa
6.Hard
d1​ = 200 mmd2​ = 100 mm12Δh = 50 mmmercuryQ = ?

A horizontal venturi meter (inlet 200 mm, throat 100 mm) carries water. A mercury U-tube manometer connected between the inlet and the throat shows a level difference of 50 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 = 200 mmd2 = 100 mmΔh = 50 mmCd = 0.99ρHg = 13 600 kg/m³g = 9.81 m/s²
Q = L/s

Answer key

  1. 1. v = 5.425 m/s
  2. 2. d = 121.5 mm
  3. 3. p2 = 258.6 kPa
  4. 4. p2 = 217.5 kPa
  5. 5. p2 = 282.6 kPa
  6. 6. Q = 28.23 L/s

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