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
vd = 25 mmh = 5.5 m

An open water tank drains through a round opening with a diameter of 25 mm in its side. The free surface is 5.5 m above the opening. Ignoring losses and the contraction of the jet, find the flow rate Q. Use g = 9.81 m/s².

h = 5.5 mg = 9.81 m/s²d = 25 mm
Q = L/s
3.Medium
Q = ?d = 30 mm, Cd​ = 0.65h = 3 m

Water drains from a large open tank through a sharp-edged orifice with a diameter of 30 mm. The water level is kept 3 m above the orifice and the discharge coefficient is 0.65. Find the flow rate Q. Use g = 9.81 m/s².

d = 30 mmh = 3 mCd = 0.65g = 9.81 m/s²
Q = L/s
4.Medium
Q = ?d = 40 mm, Cd​ = 0.61h = 4.5 m

Water drains from a large open tank through a sharp-edged orifice with a diameter of 40 mm. The water level is kept 4.5 m above the orifice and the discharge coefficient is 0.61. Find the flow rate Q. Use g = 9.81 m/s².

d = 40 mmh = 4.5 mCd = 0.61g = 9.81 m/s²
Q = L/s
5.Hard
C212 m1.5 md = 25 mmpC​ = ?

A hose with an inner diameter of 25 mm siphons water from an open tank. The highest point C of the hose is 2 m above the water surface, and the outlet (open to the air) is 1.5 m below the water surface. Ignore losses and take g = 9.81 m/s². Find the absolute pressure pC at point C. The atmospheric pressure is 101.3 kPa.

d = 25 mmzC = +2 mz2 = −1.5 mg = 9.81 m/s²patm = 101.3 kPa
pC = kPa
6.Hard
pair​ = 130 kPav = ?d = 30 mmh = 1.5 m

A closed water tank has compressed air above the water at a gauge pressure of 130 kPa. Water leaves through an opening with a diameter of 30 mm, 1.5 m below the water surface, into the open air. Ignoring losses, find the jet velocity v. Use g = 9.81 m/s².

pair = 130 kPa (gauge)h = 1.5 md = 30 mmρ = 1000 kg/m³g = 9.81 m/s²
v = m/s

Answer key

  1. 1. v2 = 4.5 m/s
  2. 2. Q = 5.099 L/s
  3. 3. Q = 3.525 L/s
  4. 4. Q = 7.203 L/s
  5. 5. pC = 66.97 kPa
  6. 6. v = 17.01 m/s

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