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​ = 1.75 m/sd2​ = 40 mm, v2​ = ?

Water flows through a pipe that narrows from 100 mm to 40 mm in diameter. The velocity in the wide section is 1.75 m/s. Find the velocity v2 in the narrow section.

d1 = 100 mmd2 = 40 mmv1 = 1.75 m/s
v2 = m/s
2.Easy
12Q = 37 L/sv = 2.5 m/s, d = ?

A water line must carry 37 L/s. To limit noise and wear, the mean velocity should be 2.5 m/s. Find the inner pipe diameter d needed.

Q = 37 L/sv = 2.5 m/s
d = mm
3.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
4.Medium
12d1​ = 75 mm, p1​ = 250 kPad2​ = 50 mm, p2​ = ?

Water flows through a horizontal pipe that narrows from 75 mm to 50 mm. In the wide section the pressure is 250 kPa and the velocity is 0.75 m/s. Ignoring losses, find the pressure p2 in the narrow section.

d1 = 75 mmd2 = 50 mmp1 = 250 kPav1 = 0.75 m/sρ = 1000 kg/m³
p2 = kPa
5.Hard
12d1​ = 100 mm, p1​ = 240 kPad2​ = 75 mm, p2​ = ?Δz = 10 m

Water flows up through a pipe that narrows from 100 mm to 75 mm while rising 10 m. At section 1 the pressure is 240 kPa and the velocity is 2.5 m/s. Ignoring losses, find the pressure p2 at section 2.

d1 = 100 mmd2 = 75 mmp1 = 240 kPav1 = 2.5 m/sΔz = 10 mρ = 1000 kg/m³
p2 = kPa
6.Hard
pair​ = 170 kPaQ = ?d = 25 mmh = 3.5 m

A closed water tank has compressed air above the water at a gauge pressure of 170 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 = 170 kPa (gauge)h = 3.5 md = 25 mmρ = 1000 kg/m³g = 9.81 m/s²
Q = L/s

Answer key

  1. 1. v2 = 10.94 m/s
  2. 2. d = 137.3 mm
  3. 3. Q = 7.203 L/s
  4. 4. p2 = 248.9 kPa
  5. 5. p2 = 135.1 kPa
  6. 6. Q = 9.923 L/s

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