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 = 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
2.Easy
12d1​ = 75 mm, v1​ = 2 m/sd2​ = 50 mm, v2​ = ?

Water flows through a pipe that narrows from 75 mm to 50 mm in diameter. The velocity in the wide section is 2 m/s. Find the velocity v2 in the narrow section.

d1 = 75 mmd2 = 50 mmv1 = 2 m/s
v2 = m/s
3.Medium
12d1​ = 75 mm, p1​ = 340 kPad2​ = 50 mm, p2​ = ?

Water flows through a horizontal pipe that narrows from 75 mm to 50 mm. In the wide section the pressure is 340 kPa and the velocity is 1 m/s. Ignoring losses, find the pressure p2 in the narrow section.

d1 = 75 mmd2 = 50 mmp1 = 340 kPav1 = 1 m/sρ = 1000 kg/m³
p2 = kPa
4.Medium
v = ?p0​pp0​ − p = 17 kPastagnation point

A pitot-static tube in a water pipe reads a difference of 17 kPa between the stagnation pressure and the static pressure. Find the water velocity v at the tip.

p0 − p = 17 kPaρ = 1000 kg/m³
v = m/s
5.Hard
12d1​ = 150 mm, p1​ = 120 kPad2​ = 100 mm, p2​ = ?Δz = 8 m

Water flows up through a pipe that narrows from 150 mm to 100 mm while rising 8 m. At section 1 the pressure is 120 kPa and the velocity is 1.75 m/s. Ignoring losses, find the pressure p2 at section 2.

d1 = 150 mmd2 = 100 mmp1 = 120 kPav1 = 1.75 m/sΔz = 8 mρ = 1000 kg/m³
p2 = kPa
6.Hard
pair​ = 160 kPav = ?d = 50 mmh = 2.5 m

A closed water tank has compressed air above the water at a gauge pressure of 160 kPa. Water leaves through an opening with a diameter of 50 mm, 2.5 m below the water surface, into the open air. Ignoring losses, find the jet velocity v. Use g = 9.81 m/s².

pair = 160 kPa (gauge)h = 2.5 md = 50 mmρ = 1000 kg/m³g = 9.81 m/s²
v = m/s

Answer key

  1. 1. v = 9.905 m/s
  2. 2. v2 = 4.5 m/s
  3. 3. p2 = 338 kPa
  4. 4. v = 5.831 m/s
  5. 5. p2 = 35.3 kPa
  6. 6. v = 19.21 m/s

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