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
12d1​ = 100 mm, v1​ = 2.25 m/sd2​ = 50 mm, v2​ = ?

Water flows through a pipe that narrows from 100 mm to 50 mm in diameter. The velocity in the wide section is 2.25 m/s. Find the velocity v2 in the narrow section.

d1 = 100 mmd2 = 50 mmv1 = 2.25 m/s
v2 = m/s
3.Medium
Q = ?d = 20 mm, Cd​ = 0.61h = 2.5 m

Water drains from a large open tank through a sharp-edged orifice with a diameter of 20 mm. The water level is kept 2.5 m above the orifice and the discharge coefficient is 0.61. Find the flow rate Q. Use g = 9.81 m/s².

d = 20 mmh = 2.5 mCd = 0.61g = 9.81 m/s²
Q = L/s
4.Medium
d1​ = 100 mmd2​ = 60 mm12p1​ − p2​ = 11 kPaQ = ?

Water flows through a horizontal venturi meter with an inlet diameter of 100 mm and a throat diameter of 60 mm. The pressure at the inlet is 11 kPa higher than at the throat. Ignoring losses, find the flow rate Q.

d1 = 100 mmd2 = 60 mmp1 − p2 = 11 kPaρ = 1000 kg/m³
Q = L/s
5.Hard
12d1​ = 75 mm, p1​ = 180 kPad2​ = 40 mm, p2​ = ?Δz = 10 m

Water flows up through a pipe that narrows from 75 mm to 40 mm while rising 10 m. At section 1 the pressure is 180 kPa and the velocity is 2.75 m/s. Ignoring losses, find the pressure p2 at section 2.

d1 = 75 mmd2 = 40 mmp1 = 180 kPav1 = 2.75 m/sΔz = 10 mρ = 1000 kg/m³
p2 = kPa
6.Hard
12d1​ = 100 mm, p1​ = 200 kPad2​ = 40 mm, p2​ = ?Δz = 10 m

Water flows up through a pipe that narrows from 100 mm to 40 mm while rising 10 m. At section 1 the pressure is 200 kPa and the velocity is 0.75 m/s. Ignoring losses, find the pressure p2 at section 2.

d1 = 100 mmd2 = 40 mmp1 = 200 kPav1 = 0.75 m/sΔz = 10 mρ = 1000 kg/m³
p2 = kPa

Answer key

  1. 1. v2 = 1.125 m/s
  2. 2. v2 = 9 m/s
  3. 3. Q = 1.342 L/s
  4. 4. Q = 14.21 L/s
  5. 5. p2 = 38.95 kPa
  6. 6. p2 = 91.19 kPa

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