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
vd = 25 mmh = 6 m

An open water tank drains through a round opening with a diameter of 25 mm in its side. The free surface is 6 m above the opening. Ignoring losses and the contraction of the jet, find the flow rate Q. Use g = 9.81 m/s².

h = 6 mg = 9.81 m/s²d = 25 mm
Q = L/s
2.Easy
v = ?h = 2.5 m

An open water tank drains through a small opening in its side. The free surface is 2.5 m above the opening. Ignoring losses, find the jet velocity v at the opening. Use g = 9.81 m/s².

h = 2.5 mg = 9.81 m/s²
v = m/s
3.Medium
12d1​ = 150 mm, p1​ = 300 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 300 kPa and the velocity is 0.5 m/s. Ignoring losses, find the pressure p2 in the narrow section.

d1 = 150 mmd2 = 50 mmp1 = 300 kPav1 = 0.5 m/sρ = 1000 kg/m³
p2 = kPa
4.Medium
12d1​ = 150 mm, p1​ = 130 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 130 kPa and the velocity is 1 m/s. Ignoring losses, find the pressure p2 in the narrow section.

d1 = 150 mmd2 = 50 mmp1 = 130 kPav1 = 1 m/sρ = 1000 kg/m³
p2 = kPa
5.Hard
12d1​ = 200 mm, p1​ = 360 kPad2​ = 75 mm, p2​ = ?Δz = 1 m

Water flows up through a pipe that narrows from 200 mm to 75 mm while rising 1 m. At section 1 the pressure is 360 kPa and the velocity is 2 m/s. Ignoring losses, find the pressure p2 at section 2.

d1 = 200 mmd2 = 75 mmp1 = 360 kPav1 = 2 m/sΔz = 1 mρ = 1000 kg/m³
p2 = kPa
6.Hard
12d1​ = 100 mm, p1​ = 400 kPad2​ = 50 mm, p2​ = ?Δz = 9 m

Water flows up through a pipe that narrows from 100 mm to 50 mm while rising 9 m. At section 1 the pressure is 400 kPa and the velocity is 3 m/s. Ignoring losses, find the pressure p2 at section 2.

d1 = 100 mmd2 = 50 mmp1 = 400 kPav1 = 3 m/sΔz = 9 mρ = 1000 kg/m³
p2 = kPa

Answer key

  1. 1. Q = 5.326 L/s
  2. 2. v = 7.004 m/s
  3. 3. p2 = 290 kPa
  4. 4. p2 = 90 kPa
  5. 5. p2 = 251.1 kPa
  6. 6. p2 = 244.2 kPa

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