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​ = 150 mm, v1​ = 0.5 m/sd2​ = 50 mm, v2​ = ?

Water flows through a pipe that narrows from 150 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 = 150 mmd2 = 50 mmv1 = 0.5 m/s
v2 = m/s
2.Easy
12Q = 36 L/sv = 1.5 m/s, d = ?

A water line must carry 36 L/s. To limit noise and wear, the mean velocity should be 1.5 m/s. Find the inner pipe diameter d needed.

Q = 36 L/sv = 1.5 m/s
d = mm
3.Medium
v = ?p0​pp0​ − p = 450 Pastagnation point

A pitot-static tube in a wind tunnel reads a difference of 450 Pa between the stagnation pressure and the static pressure. The air density is 1.2 kg/m³. Find the air speed v.

p0 − p = 450 Paρ = 1.2 kg/m³
v = m/s
4.Medium
12d1​ = 100 mm, p1​ = 400 kPad2​ = 75 mm, p2​ = ?

Water flows through a horizontal pipe that narrows from 100 mm to 75 mm. In the wide section the pressure is 400 kPa and the velocity is 1.75 m/s. Ignoring losses, find the pressure p2 in the narrow section.

d1 = 100 mmd2 = 75 mmp1 = 400 kPav1 = 1.75 m/sρ = 1000 kg/m³
p2 = kPa
5.Hard
pair​ = 120 kPav = ?d = 25 mmh = 2 m

A closed water tank has compressed air above the water at a gauge pressure of 120 kPa. Water leaves through an opening with a diameter of 25 mm, 2 m below the water surface, into the open air. Ignoring losses, find the jet velocity v. Use g = 9.81 m/s².

pair = 120 kPa (gauge)h = 2 md = 25 mmρ = 1000 kg/m³g = 9.81 m/s²
v = m/s
6.Hard
d1​ = 100 mmd2​ = 50 mm12Δh = 120 mmmercuryQ = ?

A horizontal venturi meter (inlet 100 mm, throat 50 mm) carries water. A mercury U-tube manometer connected between the inlet and the throat shows a level difference of 120 mm. The discharge coefficient is 0.95. Find the flow rate Q. Use ρ = 1000 kg/m³ for water, 13 600 kg/m³ for mercury and g = 9.81 m/s².

d1 = 100 mmd2 = 50 mmΔh = 120 mmCd = 0.95ρHg = 13 600 kg/m³g = 9.81 m/s²
Q = L/s

Answer key

  1. 1. v2 = 4.5 m/s
  2. 2. d = 174.8 mm
  3. 3. v = 27.39 m/s
  4. 4. p2 = 396.7 kPa
  5. 5. v = 16.71 m/s
  6. 6. Q = 10.49 L/s

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