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
12d1​ = 75 mm, v1​ = 2.5 m/sd2​ = 40 mm

Water flows at 2.5 m/s through the wide section of the pipe, which has a diameter of 75 mm. Find the volume flow rate Q.

d1 = 75 mmd2 = 40 mmv1 = 2.5 m/s
Q = L/s
2.Easy
v = ?h = 5 m

An open water tank drains through a small opening in its side. The free surface is 5 m above the opening. Ignoring losses, find the jet velocity v at the opening. Use g = 9.81 m/s².

h = 5 mg = 9.81 m/s²
v = m/s
3.Medium
Q = ?d = 30 mm, Cd​ = 0.64h = 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 0.64. Find the flow rate Q. Use g = 9.81 m/s².

d = 30 mmh = 1 mCd = 0.64g = 9.81 m/s²
Q = L/s
4.Medium
12d1​ = 150 mm, p1​ = 140 kPad2​ = 75 mm, p2​ = ?

Water flows through a horizontal pipe that narrows from 150 mm to 75 mm. In the wide section the pressure is 140 kPa and the velocity is 1 m/s. Ignoring losses, find the pressure p2 in the narrow section.

d1 = 150 mmd2 = 75 mmp1 = 140 kPav1 = 1 m/sρ = 1000 kg/m³
p2 = kPa
5.Hard
12d1​ = 150 mm, p1​ = 230 kPad2​ = 75 mm, p2​ = ?Δz = 3 m

Water flows up through a pipe that narrows from 150 mm to 75 mm while rising 3 m. At section 1 the pressure is 230 kPa and the velocity is 1.5 m/s. Ignoring losses, find the pressure p2 at section 2.

d1 = 150 mmd2 = 75 mmp1 = 230 kPav1 = 1.5 m/sΔz = 3 mρ = 1000 kg/m³
p2 = kPa
6.Hard
12d1​ = 100 mm, p1​ = 220 kPad2​ = 40 mm, p2​ = ?Δz = 5 m

Water flows up through a pipe that narrows from 100 mm to 40 mm while rising 5 m. At section 1 the pressure is 220 kPa and the velocity is 2.25 m/s. Ignoring losses, find the pressure p2 at section 2.

d1 = 100 mmd2 = 40 mmp1 = 220 kPav1 = 2.25 m/sΔz = 5 mρ = 1000 kg/m³
p2 = kPa

Answer key

  1. 1. Q = 11.04 L/s
  2. 2. v = 9.905 m/s
  3. 3. Q = 2.004 L/s
  4. 4. p2 = 132.5 kPa
  5. 5. p2 = 183.7 kPa
  6. 6. p2 = 74.6 kPa

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