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​ = 100 mm, v1​ = 0.5 m/sd2​ = 40 mm, v2​ = ?

Water flows through a pipe that narrows from 100 mm to 40 mm in diameter. The velocity in the wide section is 0.5 m/s. Find the velocity v2 in the narrow section.

d1 = 100 mmd2 = 40 mmv1 = 0.5 m/s
v2 = m/s
2.Easy
vd = 30 mmh = 2 m

An open water tank drains through a round opening with a diameter of 30 mm in its side. The free surface is 2 m above the opening. Ignoring losses and the contraction of the jet, find the flow rate Q. Use g = 9.81 m/s².

h = 2 mg = 9.81 m/s²d = 30 mm
Q = L/s
3.Medium
12d1​ = 200 mm, p1​ = 380 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 380 kPa and the velocity is 1.25 m/s. Ignoring losses, find the pressure p2 in the narrow section.

d1 = 200 mmd2 = 100 mmp1 = 380 kPav1 = 1.25 m/sρ = 1000 kg/m³
p2 = kPa
4.Medium
v = ?p0​pp0​ − p = 20 kPastagnation point

A pitot-static tube in a water pipe reads a difference of 20 kPa between the stagnation pressure and the static pressure. Find the water velocity v at the tip.

p0 − p = 20 kPaρ = 1000 kg/m³
v = m/s
5.Hard
pair​ = 80 kPaQ = ?d = 30 mmh = 3 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 30 mm, 3 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 = 3 md = 30 mmρ = 1000 kg/m³g = 9.81 m/s²
Q = L/s
6.Hard
pair​ = 110 kPav = ?d = 40 mmh = 4 m

A closed water tank has compressed air above the water at a gauge pressure of 110 kPa. Water leaves through an opening with a diameter of 40 mm, 4 m below the water surface, into the open air. Ignoring losses, find the jet velocity v. Use g = 9.81 m/s².

pair = 110 kPa (gauge)h = 4 md = 40 mmρ = 1000 kg/m³g = 9.81 m/s²
v = m/s

Answer key

  1. 1. v2 = 3.125 m/s
  2. 2. Q = 4.428 L/s
  3. 3. p2 = 368.3 kPa
  4. 4. v = 6.325 m/s
  5. 5. Q = 10.46 L/s
  6. 6. v = 17.28 m/s

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