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​ = 200 mm, v1​ = 2.25 m/sd2​ = 100 mm

Water flows at 2.25 m/s through the wide section of the pipe, which has a diameter of 200 mm. Find the volume flow rate Q.

d1 = 200 mmd2 = 100 mmv1 = 2.25 m/s
Q = L/s
2.Easy
12d1​ = 100 mm, v1​ = 1.25 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 1.25 m/s. Find the velocity v2 in the narrow section.

d1 = 100 mmd2 = 40 mmv1 = 1.25 m/s
v2 = m/s
3.Medium
12d1​ = 100 mm, p1​ = 140 kPad2​ = 25 mm, p2​ = ?

Water flows through a horizontal pipe that narrows from 100 mm to 25 mm. In the wide section the pressure is 140 kPa and the velocity is 0.5 m/s. Ignoring losses, find the pressure p2 in the narrow section.

d1 = 100 mmd2 = 25 mmp1 = 140 kPav1 = 0.5 m/sρ = 1000 kg/m³
p2 = kPa
4.Medium
Q = ?d = 20 mm, Cd​ = 0.62h = 5.5 m

Water drains from a large open tank through a sharp-edged orifice with a diameter of 20 mm. The water level is kept 5.5 m above the orifice and the discharge coefficient is 0.62. Find the flow rate Q. Use g = 9.81 m/s².

d = 20 mmh = 5.5 mCd = 0.62g = 9.81 m/s²
Q = L/s
5.Hard
12d1​ = 100 mm, p1​ = 150 kPad2​ = 40 mm, p2​ = ?Δz = 6 m

Water flows up through a pipe that narrows from 100 mm to 40 mm while rising 6 m. At section 1 the pressure is 150 kPa and the velocity is 1 m/s. Ignoring losses, find the pressure p2 at section 2.

d1 = 100 mmd2 = 40 mmp1 = 150 kPav1 = 1 m/sΔz = 6 mρ = 1000 kg/m³
p2 = kPa
6.Hard
12d1​ = 200 mm, p1​ = 340 kPad2​ = 75 mm, p2​ = ?Δz = 6 m

Water flows up through a pipe that narrows from 200 mm to 75 mm while rising 6 m. At section 1 the pressure is 340 kPa and the velocity is 0.75 m/s. Ignoring losses, find the pressure p2 at section 2.

d1 = 200 mmd2 = 75 mmp1 = 340 kPav1 = 0.75 m/sΔz = 6 mρ = 1000 kg/m³
p2 = kPa

Answer key

  1. 1. Q = 70.69 L/s
  2. 2. v2 = 7.813 m/s
  3. 3. p2 = 108.1 kPa
  4. 4. Q = 2.023 L/s
  5. 5. p2 = 72.11 kPa
  6. 6. p2 = 267.2 kPa

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