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 = 4.5 m

An open water tank drains through a round opening with a diameter of 25 mm in its side. The free surface is 4.5 m above the opening. Ignoring losses and the contraction of the jet, find the flow rate Q. Use g = 9.81 m/s².

h = 4.5 mg = 9.81 m/s²d = 25 mm
Q = L/s
2.Easy
12d1​ = 200 mm, v1​ = 1.25 m/sd2​ = 75 mm

Water flows at 1.25 m/s through the wide section of the pipe, which has a diameter of 200 mm. Find the volume flow rate Q.

d1 = 200 mmd2 = 75 mmv1 = 1.25 m/s
Q = L/s
3.Medium
12d1​ = 100 mm, p1​ = 180 kPad2​ = 40 mm, p2​ = ?

Water flows through a horizontal pipe that narrows from 100 mm to 40 mm. In the wide section the pressure is 180 kPa and the velocity is 1.75 m/s. Ignoring losses, find the pressure p2 in the narrow section.

d1 = 100 mmd2 = 40 mmp1 = 180 kPav1 = 1.75 m/sρ = 1000 kg/m³
p2 = kPa
4.Medium
12d1​ = 200 mm, p1​ = 120 kPad2​ = 100 mm, p2​ = ?

Water flows through a horizontal pipe that narrows from 200 mm to 100 mm. In the wide section the pressure is 120 kPa and the velocity is 1.5 m/s. Ignoring losses, find the pressure p2 in the narrow section.

d1 = 200 mmd2 = 100 mmp1 = 120 kPav1 = 1.5 m/sρ = 1000 kg/m³
p2 = kPa
5.Hard
12d1​ = 150 mm, p1​ = 280 kPad2​ = 100 mm, p2​ = ?Δz = 9 m

Water flows up through a pipe that narrows from 150 mm to 100 mm while rising 9 m. At section 1 the pressure is 280 kPa and the velocity is 2 m/s. Ignoring losses, find the pressure p2 at section 2.

d1 = 150 mmd2 = 100 mmp1 = 280 kPav1 = 2 m/sΔz = 9 mρ = 1000 kg/m³
p2 = kPa
6.Hard
pair​ = 80 kPaQ = ?d = 20 mmh = 5 m

A closed water tank has compressed air above the water at a gauge pressure of 80 kPa. Water leaves through an opening with a diameter of 20 mm, 5 m below the water surface, into the open air. Ignoring losses, find the flow rate Q. Use g = 9.81 m/s².

pair = 80 kPa (gauge)h = 5 md = 20 mmρ = 1000 kg/m³g = 9.81 m/s²
Q = L/s

Answer key

  1. 1. Q = 4.612 L/s
  2. 2. Q = 39.27 L/s
  3. 3. p2 = 121.7 kPa
  4. 4. p2 = 103.1 kPa
  5. 5. p2 = 183.6 kPa
  6. 6. Q = 5.047 L/s

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