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​ = 2 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 2 m/s. Find the velocity v2 in the narrow section.

d1 = 100 mmd2 = 40 mmv1 = 2 m/s
v2 = m/s
2.Easy
12d1​ = 100 mm, v1​ = 1 m/sd2​ = 50 mm

Water flows at 1 m/s through the wide section of the pipe, which has a diameter of 100 mm. Find the volume flow rate Q.

d1 = 100 mmd2 = 50 mmv1 = 1 m/s
Q = L/s
3.Medium
Q = ?d = 25 mm, Cd​ = 0.61h = 6 m

Water drains from a large open tank through a sharp-edged orifice with a diameter of 25 mm. The water level is kept 6 m above the orifice and the discharge coefficient is 0.61. Find the flow rate Q. Use g = 9.81 m/s².

d = 25 mmh = 6 mCd = 0.61g = 9.81 m/s²
Q = L/s
4.Medium
12d1​ = 200 mm, p1​ = 160 kPad2​ = 100 mm, p2​ = ?

Water flows through a horizontal pipe that narrows from 200 mm to 100 mm. In the wide section the pressure is 160 kPa and the velocity is 2 m/s. Ignoring losses, find the pressure p2 in the narrow section.

d1 = 200 mmd2 = 100 mmp1 = 160 kPav1 = 2 m/sρ = 1000 kg/m³
p2 = kPa
5.Hard
12d1​ = 75 mm, p1​ = 250 kPad2​ = 40 mm, p2​ = ?Δz = 5 m

Water flows up through a pipe that narrows from 75 mm to 40 mm while rising 5 m. At section 1 the pressure is 250 kPa and the velocity is 1.75 m/s. Ignoring losses, find the pressure p2 at section 2.

d1 = 75 mmd2 = 40 mmp1 = 250 kPav1 = 1.75 m/sΔz = 5 mρ = 1000 kg/m³
p2 = kPa
6.Hard
12d1​ = 200 mm, p1​ = 290 kPad2​ = 100 mm, p2​ = ?Δz = 4 m

Water flows up through a pipe that narrows from 200 mm to 100 mm while rising 4 m. At section 1 the pressure is 290 kPa and the velocity is 2 m/s. Ignoring losses, find the pressure p2 at section 2.

d1 = 200 mmd2 = 100 mmp1 = 290 kPav1 = 2 m/sΔz = 4 mρ = 1000 kg/m³
p2 = kPa

Answer key

  1. 1. v2 = 12.5 m/s
  2. 2. Q = 7.854 L/s
  3. 3. Q = 3.249 L/s
  4. 4. p2 = 130 kPa
  5. 5. p2 = 183.6 kPa
  6. 6. p2 = 220.8 kPa

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