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​ = 0.75 m/sd2​ = 50 mm, v2​ = ?

Water flows through a pipe that narrows from 100 mm to 50 mm in diameter. The velocity in the wide section is 0.75 m/s. Find the velocity v2 in the narrow section.

d1 = 100 mmd2 = 50 mmv1 = 0.75 m/s
v2 = m/s
2.Easy
12d1​ = 100 mm, v1​ = 2.5 m/sd2​ = 75 mm

Water flows at 2.5 m/s through the wide section of the pipe, which has a diameter of 100 mm. Find the volume flow rate Q.

d1 = 100 mmd2 = 75 mmv1 = 2.5 m/s
Q = L/s
3.Medium
v = ?p0​pp0​ − p = 33 kPastagnation point

A pitot-static tube in a water pipe reads a difference of 33 kPa between the stagnation pressure and the static pressure. Find the water velocity v at the tip.

p0 − p = 33 kPaρ = 1000 kg/m³
v = m/s
4.Medium
Q = ?d = 25 mm, Cd​ = 0.64h = 5 m

Water drains from a large open tank through a sharp-edged orifice with a diameter of 25 mm. The water level is kept 5 m above the orifice and the discharge coefficient is 0.64. Find the flow rate Q. Use g = 9.81 m/s².

d = 25 mmh = 5 mCd = 0.64g = 9.81 m/s²
Q = L/s
5.Hard
pair​ = 110 kPaQ = ?d = 50 mmh = 2.5 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 50 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 = 110 kPa (gauge)h = 2.5 md = 50 mmρ = 1000 kg/m³g = 9.81 m/s²
Q = L/s
6.Hard
pair​ = 70 kPaQ = ?d = 40 mmh = 4.5 m

A closed water tank has compressed air above the water at a gauge pressure of 70 kPa. Water leaves through an opening with a diameter of 40 mm, 4.5 m below the water surface, into the open air. Ignoring losses, find the flow rate Q. Use g = 9.81 m/s².

pair = 70 kPa (gauge)h = 4.5 md = 40 mmρ = 1000 kg/m³g = 9.81 m/s²
Q = L/s

Answer key

  1. 1. v2 = 3 m/s
  2. 2. Q = 19.63 L/s
  3. 3. v = 8.124 m/s
  4. 4. Q = 3.112 L/s
  5. 5. Q = 32.21 L/s
  6. 6. Q = 18.99 L/s

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