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​ = 0.5 m/sd2​ = 75 mm, v2​ = ?

Water flows through a pipe that narrows from 200 mm to 75 mm in diameter. The velocity in the wide section is 0.5 m/s. Find the velocity v2 in the narrow section.

d1 = 200 mmd2 = 75 mmv1 = 0.5 m/s
v2 = m/s
2.Easy
12d1​ = 150 mm, v1​ = 1.75 m/sd2​ = 100 mm, v2​ = ?

Water flows through a pipe that narrows from 150 mm to 100 mm in diameter. The velocity in the wide section is 1.75 m/s. Find the velocity v2 in the narrow section.

d1 = 150 mmd2 = 100 mmv1 = 1.75 m/s
v2 = m/s
3.Medium
Q = ?d = 20 mm, Cd​ = 0.61h = 4 m

Water drains from a large open tank through a sharp-edged orifice with a diameter of 20 mm. The water level is kept 4 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 = 4 mCd = 0.61g = 9.81 m/s²
Q = L/s
4.Medium
v = ?p0​pp0​ − p = 1200 Pastagnation point

A pitot-static tube in a wind tunnel reads a difference of 1200 Pa between the stagnation pressure and the static pressure. The air density is 1.2 kg/m³. Find the air speed v.

p0 − p = 1200 Paρ = 1.2 kg/m³
v = m/s
5.Hard
12d1​ = 200 mm, p1​ = 210 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 210 kPa and the velocity is 0.5 m/s. Ignoring losses, find the pressure p2 at section 2.

d1 = 200 mmd2 = 100 mmp1 = 210 kPav1 = 0.5 m/sΔz = 4 mρ = 1000 kg/m³
p2 = kPa
6.Hard
12d1​ = 100 mm, p1​ = 390 kPad2​ = 40 mm, p2​ = ?Δz = 2 m

Water flows up through a pipe that narrows from 100 mm to 40 mm while rising 2 m. At section 1 the pressure is 390 kPa and the velocity is 1.25 m/s. Ignoring losses, find the pressure p2 at section 2.

d1 = 100 mmd2 = 40 mmp1 = 390 kPav1 = 1.25 m/sΔz = 2 mρ = 1000 kg/m³
p2 = kPa

Answer key

  1. 1. v2 = 3.556 m/s
  2. 2. v2 = 3.938 m/s
  3. 3. Q = 1.698 L/s
  4. 4. v = 44.72 m/s
  5. 5. p2 = 168.9 kPa
  6. 6. p2 = 340.6 kPa

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