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​ = 3 m/sd2​ = 75 mm, v2​ = ?

Water flows through a pipe that narrows from 100 mm to 75 mm in diameter. The velocity in the wide section is 3 m/s. Find the velocity v2 in the narrow section.

d1 = 100 mmd2 = 75 mmv1 = 3 m/s
v2 = m/s
2.Easy
12d = 80 mm, v = 1.75 m/sṁ = ?

Water (ρ = 1000 kg/m³) flows at 1.75 m/s through a pipe with an inner diameter of 80 mm. Find the mass flow rate ṁ.

ρ = 1000 kg/m³v = 1.75 m/sd = 80 mm
ṁ = kg/s
3.Medium
v = ?p0​pp0​ − p = 10 kPastagnation point

A pitot-static tube in a water pipe reads a difference of 10 kPa between the stagnation pressure and the static pressure. Find the water velocity v at the tip.

p0 − p = 10 kPaρ = 1000 kg/m³
v = m/s
4.Medium
12d1​ = 75 mm, p1​ = 240 kPad2​ = 40 mm, p2​ = ?

Water flows through a horizontal pipe that narrows from 75 mm to 40 mm. In the wide section the pressure is 240 kPa and the velocity is 0.75 m/s. Ignoring losses, find the pressure p2 in the narrow section.

d1 = 75 mmd2 = 40 mmp1 = 240 kPav1 = 0.75 m/sρ = 1000 kg/m³
p2 = kPa
5.Hard
12d1​ = 200 mm, p1​ = 240 kPad2​ = 100 mm, p2​ = ?Δz = 8 m

Water flows up through a pipe that narrows from 200 mm to 100 mm while rising 8 m. At section 1 the pressure is 240 kPa and the velocity is 2.5 m/s. Ignoring losses, find the pressure p2 at section 2.

d1 = 200 mmd2 = 100 mmp1 = 240 kPav1 = 2.5 m/sΔz = 8 mρ = 1000 kg/m³
p2 = kPa
6.Hard
12d1​ = 150 mm, p1​ = 350 kPad2​ = 40 mm, p2​ = ?Δz = 1 m

Water flows up through a pipe that narrows from 150 mm to 40 mm while rising 1 m. At section 1 the pressure is 350 kPa and the velocity is 0.5 m/s. Ignoring losses, find the pressure p2 at section 2.

d1 = 150 mmd2 = 40 mmp1 = 350 kPav1 = 0.5 m/sΔz = 1 mρ = 1000 kg/m³
p2 = kPa

Answer key

  1. 1. v2 = 5.333 m/s
  2. 2. ṁ = 8.796 kg/s
  3. 3. v = 4.472 m/s
  4. 4. p2 = 236.8 kPa
  5. 5. p2 = 114.6 kPa
  6. 6. p2 = 315.6 kPa

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