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
12d = 40 mm, v = 4 m/sṁ = ?

Seawater (ρ = 1025 kg/m³) flows at 4 m/s through a pipe with an inner diameter of 40 mm. Find the mass flow rate ṁ.

ρ = 1025 kg/m³v = 4 m/sd = 40 mm
ṁ = kg/s
2.Easy
12d = 40 mm, v = 2.75 m/sṁ = ?

Oil (ρ = 880 kg/m³) flows at 2.75 m/s through a pipe with an inner diameter of 40 mm. Find the mass flow rate ṁ.

ρ = 880 kg/m³v = 2.75 m/sd = 40 mm
ṁ = kg/s
3.Medium
v = ?p0​pp0​ − p = 1000 Pastagnation point

A pitot-static tube in a wind tunnel reads a difference of 1000 Pa between the stagnation pressure and the static pressure. The air density is 1.2 kg/m³. Find the air speed v.

p0 − p = 1000 Paρ = 1.2 kg/m³
v = m/s
4.Medium
v = ?p0​pp0​ − p = 38 kPastagnation point

A pitot-static tube in a water pipe reads a difference of 38 kPa between the stagnation pressure and the static pressure. Find the water velocity v at the tip.

p0 − p = 38 kPaρ = 1000 kg/m³
v = m/s
5.Hard
12d1​ = 200 mm, p1​ = 180 kPad2​ = 75 mm, p2​ = ?Δz = 10 m

Water flows up through a pipe that narrows from 200 mm to 75 mm while rising 10 m. At section 1 the pressure is 180 kPa and the velocity is 0.75 m/s. Ignoring losses, find the pressure p2 at section 2.

d1 = 200 mmd2 = 75 mmp1 = 180 kPav1 = 0.75 m/sΔz = 10 mρ = 1000 kg/m³
p2 = kPa
6.Hard
12d1​ = 200 mm, p1​ = 350 kPad2​ = 50 mm, p2​ = ?Δz = 2 m

Water flows up through a pipe that narrows from 200 mm to 50 mm while rising 2 m. At section 1 the pressure is 350 kPa and the velocity is 0.75 m/s. Ignoring losses, find the pressure p2 at section 2.

d1 = 200 mmd2 = 50 mmp1 = 350 kPav1 = 0.75 m/sΔz = 2 mρ = 1000 kg/m³
p2 = kPa

Answer key

  1. 1. ṁ = 5.152 kg/s
  2. 2. ṁ = 3.041 kg/s
  3. 3. v = 40.82 m/s
  4. 4. v = 8.718 m/s
  5. 5. p2 = 67.96 kPa
  6. 6. p2 = 258.7 kPa

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