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​ = 75 mm, v1​ = 0.5 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 0.5 m/s. Find the velocity v2 in the narrow section.

d1 = 75 mmd2 = 50 mmv1 = 0.5 m/s
v2 = m/s
2.Easy
12d1​ = 150 mm, v1​ = 0.75 m/sd2​ = 100 mm, v2​ = ?

Water flows through a pipe that narrows from 150 mm to 100 mm in diameter. The velocity in the wide section is 0.75 m/s. Find the velocity v2 in the narrow section.

d1 = 150 mmd2 = 100 mmv1 = 0.75 m/s
v2 = m/s
3.Medium
12d1​ = 150 mm, p1​ = 350 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 350 kPa and the velocity is 1.5 m/s. Ignoring losses, find the pressure p2 in the narrow section.

d1 = 150 mmd2 = 50 mmp1 = 350 kPav1 = 1.5 m/sρ = 1000 kg/m³
p2 = kPa
4.Medium
v = ?p0​pp0​ − p = 350 Pastagnation point

A pitot-static tube in a wind tunnel reads a difference of 350 Pa between the stagnation pressure and the static pressure. The air density is 1.2 kg/m³. Find the air speed v.

p0 − p = 350 Paρ = 1.2 kg/m³
v = m/s
5.Hard
12d1​ = 75 mm, p1​ = 260 kPad2​ = 40 mm, p2​ = ?Δz = 8 m

Water flows up through a pipe that narrows from 75 mm to 40 mm while rising 8 m. At section 1 the pressure is 260 kPa and the velocity is 0.5 m/s. Ignoring losses, find the pressure p2 at section 2.

d1 = 75 mmd2 = 40 mmp1 = 260 kPav1 = 0.5 m/sΔz = 8 mρ = 1000 kg/m³
p2 = kPa
6.Hard
pair​ = 40 kPaQ = ?d = 25 mmh = 3.5 m

A closed water tank has compressed air above the water at a gauge pressure of 40 kPa. Water leaves through an opening with a diameter of 25 mm, 3.5 m below the water surface, into the open air. Ignoring losses, find the flow rate Q. Use g = 9.81 m/s².

pair = 40 kPa (gauge)h = 3.5 md = 25 mmρ = 1000 kg/m³g = 9.81 m/s²
Q = L/s

Answer key

  1. 1. v2 = 1.125 m/s
  2. 2. v2 = 1.688 m/s
  3. 3. p2 = 260 kPa
  4. 4. v = 24.15 m/s
  5. 5. p2 = 180.1 kPa
  6. 6. Q = 5.985 L/s

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