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 = 3.5 m

An open water tank drains through a small opening in its side. The free surface is 3.5 m above the opening. Ignoring losses, find the jet velocity v at the opening. Use g = 9.81 m/s².

h = 3.5 mg = 9.81 m/s²
v = m/s
2.Easy
12d1​ = 200 mm, v1​ = 1 m/sd2​ = 100 mm

Water flows at 1 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 = 100 mmv1 = 1 m/s
Q = L/s
3.Medium
12d1​ = 100 mm, p1​ = 330 kPad2​ = 50 mm, p2​ = ?

Water flows through a horizontal pipe that narrows from 100 mm to 50 mm. In the wide section the pressure is 330 kPa and the velocity is 0.75 m/s. Ignoring losses, find the pressure p2 in the narrow section.

d1 = 100 mmd2 = 50 mmp1 = 330 kPav1 = 0.75 m/sρ = 1000 kg/m³
p2 = kPa
4.Medium
12d1​ = 75 mm, p1​ = 140 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 140 kPa and the velocity is 0.5 m/s. Ignoring losses, find the pressure p2 in the narrow section.

d1 = 75 mmd2 = 40 mmp1 = 140 kPav1 = 0.5 m/sρ = 1000 kg/m³
p2 = kPa
5.Hard
pair​ = 30 kPav = ?d = 25 mmh = 1 m

A closed water tank has compressed air above the water at a gauge pressure of 30 kPa. Water leaves through an opening with a diameter of 25 mm, 1 m below the water surface, into the open air. Ignoring losses, find the jet velocity v. Use g = 9.81 m/s².

pair = 30 kPa (gauge)h = 1 md = 25 mmρ = 1000 kg/m³g = 9.81 m/s²
v = m/s
6.Hard
12d1​ = 150 mm, p1​ = 260 kPad2​ = 50 mm, p2​ = ?Δz = 3 m

Water flows up through a pipe that narrows from 150 mm to 50 mm while rising 3 m. At section 1 the pressure is 260 kPa and the velocity is 1.25 m/s. Ignoring losses, find the pressure p2 at section 2.

d1 = 150 mmd2 = 50 mmp1 = 260 kPav1 = 1.25 m/sΔz = 3 mρ = 1000 kg/m³
p2 = kPa

Answer key

  1. 1. v = 8.287 m/s
  2. 2. Q = 31.42 L/s
  3. 3. p2 = 325.8 kPa
  4. 4. p2 = 138.6 kPa
  5. 5. v = 8.923 m/s
  6. 6. p2 = 168.1 kPa

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