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​ = 2.75 m/sd2​ = 50 mm

Water flows at 2.75 m/s through the wide section of the pipe, which has a diameter of 75 mm. Find the volume flow rate Q.

d1 = 75 mmd2 = 50 mmv1 = 2.75 m/s
Q = L/s
2.Easy
12d1​ = 75 mm, v1​ = 1 m/sd2​ = 40 mm

Water flows at 1 m/s through the wide section of the pipe, which has a diameter of 75 mm. Find the volume flow rate Q.

d1 = 75 mmd2 = 40 mmv1 = 1 m/s
Q = L/s
3.Medium
12d1​ = 150 mm, p1​ = 150 kPad2​ = 100 mm, p2​ = ?

Water flows through a horizontal pipe that narrows from 150 mm to 100 mm. In the wide section the pressure is 150 kPa and the velocity is 1 m/s. Ignoring losses, find the pressure p2 in the narrow section.

d1 = 150 mmd2 = 100 mmp1 = 150 kPav1 = 1 m/sρ = 1000 kg/m³
p2 = kPa
4.Medium
Q = ?d = 25 mm, Cd​ = 0.63h = 4 m

Water drains from a large open tank through a sharp-edged orifice with a diameter of 25 mm. The water level is kept 4 m above the orifice and the discharge coefficient is 0.63. Find the flow rate Q. Use g = 9.81 m/s².

d = 25 mmh = 4 mCd = 0.63g = 9.81 m/s²
Q = L/s
5.Hard
12d1​ = 75 mm, p1​ = 220 kPad2​ = 50 mm, p2​ = ?Δz = 8 m

Water flows up through a pipe that narrows from 75 mm to 50 mm while rising 8 m. At section 1 the pressure is 220 kPa and the velocity is 1 m/s. Ignoring losses, find the pressure p2 at section 2.

d1 = 75 mmd2 = 50 mmp1 = 220 kPav1 = 1 m/sΔz = 8 mρ = 1000 kg/m³
p2 = kPa
6.Hard
12d1​ = 75 mm, p1​ = 170 kPad2​ = 25 mm, p2​ = ?Δz = 9 m

Water flows up through a pipe that narrows from 75 mm to 25 mm while rising 9 m. At section 1 the pressure is 170 kPa and the velocity is 0.5 m/s. Ignoring losses, find the pressure p2 at section 2.

d1 = 75 mmd2 = 25 mmp1 = 170 kPav1 = 0.5 m/sΔz = 9 mρ = 1000 kg/m³
p2 = kPa

Answer key

  1. 1. Q = 12.15 L/s
  2. 2. Q = 4.418 L/s
  3. 3. p2 = 148 kPa
  4. 4. Q = 2.74 L/s
  5. 5. p2 = 139.5 kPa
  6. 6. p2 = 71.71 kPa

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