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
12Q = 4 L/sv = 1 m/s, d = ?

A water line must carry 4 L/s. To limit noise and wear, the mean velocity should be 1 m/s. Find the inner pipe diameter d needed.

Q = 4 L/sv = 1 m/s
d = mm
2.Easy
12d = 25 mm, v = 3.25 m/sṁ = ?

Glycerin (ρ = 1260 kg/m³) flows at 3.25 m/s through a pipe with an inner diameter of 25 mm. Find the mass flow rate ṁ.

ρ = 1260 kg/m³v = 3.25 m/sd = 25 mm
ṁ = kg/s
3.Medium
12d1​ = 100 mm, p1​ = 280 kPad2​ = 75 mm, p2​ = ?

Water flows through a horizontal pipe that narrows from 100 mm to 75 mm. In the wide section the pressure is 280 kPa and the velocity is 0.5 m/s. Ignoring losses, find the pressure p2 in the narrow section.

d1 = 100 mmd2 = 75 mmp1 = 280 kPav1 = 0.5 m/sρ = 1000 kg/m³
p2 = kPa
4.Medium
12d1​ = 150 mm, p1​ = 350 kPad2​ = 50 mm, p2​ = ?

Water flows through a horizontal pipe that narrows from 150 mm to 50 mm. In the wide section the pressure is 350 kPa and the velocity is 1 m/s. Ignoring losses, find the pressure p2 in the narrow section.

d1 = 150 mmd2 = 50 mmp1 = 350 kPav1 = 1 m/sρ = 1000 kg/m³
p2 = kPa
5.Hard
12d1​ = 200 mm, p1​ = 110 kPad2​ = 50 mm, p2​ = ?Δz = 4 m

Water flows up through a pipe that narrows from 200 mm to 50 mm while rising 4 m. At section 1 the pressure is 110 kPa and the velocity is 0.5 m/s. Ignoring losses, find the pressure p2 at section 2.

d1 = 200 mmd2 = 50 mmp1 = 110 kPav1 = 0.5 m/sΔz = 4 mρ = 1000 kg/m³
p2 = kPa
6.Hard
12d1​ = 100 mm, p1​ = 380 kPad2​ = 50 mm, p2​ = ?Δz = 5 m

Water flows up through a pipe that narrows from 100 mm to 50 mm while rising 5 m. At section 1 the pressure is 380 kPa and the velocity is 0.75 m/s. Ignoring losses, find the pressure p2 at section 2.

d1 = 100 mmd2 = 50 mmp1 = 380 kPav1 = 0.75 m/sΔz = 5 mρ = 1000 kg/m³
p2 = kPa

Answer key

  1. 1. d = 71.36 mm
  2. 2. ṁ = 2.01 kg/s
  3. 3. p2 = 279.7 kPa
  4. 4. p2 = 310 kPa
  5. 5. p2 = 38.88 kPa
  6. 6. p2 = 326.7 kPa

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