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​ = 40 mm, v2​ = ?

Water flows through a pipe that narrows from 75 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 = 75 mmd2 = 40 mmv1 = 0.5 m/s
v2 = m/s
2.Easy
12Q = 16 L/sv = 1.5 m/s, d = ?

A water line must carry 16 L/s. To limit noise and wear, the mean velocity should be 1.5 m/s. Find the inner pipe diameter d needed.

Q = 16 L/sv = 1.5 m/s
d = mm
3.Medium
v = ?p0​pp0​ − p = 14 kPastagnation point

A pitot-static tube in a water pipe reads a difference of 14 kPa between the stagnation pressure and the static pressure. Find the water velocity v at the tip.

p0 − p = 14 kPaρ = 1000 kg/m³
v = m/s
4.Medium
Q = ?d = 30 mm, Cd​ = 0.62h = 2.5 m

Water drains from a large open tank through a sharp-edged orifice with a diameter of 30 mm. The water level is kept 2.5 m above the orifice and the discharge coefficient is 0.62. Find the flow rate Q. Use g = 9.81 m/s².

d = 30 mmh = 2.5 mCd = 0.62g = 9.81 m/s²
Q = L/s
5.Hard
pair​ = 190 kPaQ = ?d = 25 mmh = 2.5 m

A closed water tank has compressed air above the water at a gauge pressure of 190 kPa. Water leaves through an opening with a diameter of 25 mm, 2.5 m below the water surface, into the open air. Ignoring losses, find the flow rate Q. Use g = 9.81 m/s².

pair = 190 kPa (gauge)h = 2.5 md = 25 mmρ = 1000 kg/m³g = 9.81 m/s²
Q = L/s
6.Hard
d1​ = 80 mmd2​ = 40 mm12Δh = 330 mmmercuryQ = ?

A horizontal venturi meter (inlet 80 mm, throat 40 mm) carries water. A mercury U-tube manometer connected between the inlet and the throat shows a level difference of 330 mm. The discharge coefficient is 0.96. 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 = 80 mmd2 = 40 mmΔh = 330 mmCd = 0.96ρHg = 13 600 kg/m³g = 9.81 m/s²
Q = L/s

Answer key

  1. 1. v2 = 1.758 m/s
  2. 2. d = 116.5 mm
  3. 3. v = 5.292 m/s
  4. 4. Q = 3.069 L/s
  5. 5. Q = 10.17 L/s
  6. 6. Q = 11.25 L/s

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