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​ = 50 mm, v2​ = ?

Water flows through a pipe that narrows from 75 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 = 75 mmd2 = 50 mmv1 = 0.5 m/s
v2 = m/s
2.Easy
12Q = 23 L/sv = 3 m/s, d = ?

A water line must carry 23 L/s. To limit noise and wear, the mean velocity should be 3 m/s. Find the inner pipe diameter d needed.

Q = 23 L/sv = 3 m/s
d = mm
3.Medium
12d1​ = 75 mm, p1​ = 300 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 300 kPa and the velocity is 3 m/s. Ignoring losses, find the pressure p2 in the narrow section.

d1 = 75 mmd2 = 50 mmp1 = 300 kPav1 = 3 m/sρ = 1000 kg/m³
p2 = kPa
4.Medium
Q = ?d = 25 mm, Cd​ = 0.6h = 1 m

Water drains from a large open tank through a sharp-edged orifice with a diameter of 25 mm. The water level is kept 1 m above the orifice and the discharge coefficient is 0.6. Find the flow rate Q. Use g = 9.81 m/s².

d = 25 mmh = 1 mCd = 0.6g = 9.81 m/s²
Q = L/s
5.Hard
12d1​ = 75 mm, p1​ = 120 kPad2​ = 40 mm, p2​ = ?Δz = 7 m

Water flows up through a pipe that narrows from 75 mm to 40 mm while rising 7 m. At section 1 the pressure is 120 kPa and the velocity is 0.5 m/s. Ignoring losses, find the pressure p2 at section 2.

d1 = 75 mmd2 = 40 mmp1 = 120 kPav1 = 0.5 m/sΔz = 7 mρ = 1000 kg/m³
p2 = kPa
6.Hard
12d1​ = 100 mm, p1​ = 250 kPad2​ = 50 mm, p2​ = ?Δz = 9 m

Water flows up through a pipe that narrows from 100 mm to 50 mm while rising 9 m. At section 1 the pressure is 250 kPa and the velocity is 2.75 m/s. Ignoring losses, find the pressure p2 at section 2.

d1 = 100 mmd2 = 50 mmp1 = 250 kPav1 = 2.75 m/sΔz = 9 mρ = 1000 kg/m³
p2 = kPa

Answer key

  1. 1. v2 = 1.125 m/s
  2. 2. d = 98.8 mm
  3. 3. p2 = 281.7 kPa
  4. 4. Q = 1.305 L/s
  5. 5. p2 = 49.91 kPa
  6. 6. p2 = 105 kPa

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