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 = 100 mm, v = 1.25 m/sṁ = ?

Seawater (ρ = 1025 kg/m³) flows at 1.25 m/s through a pipe with an inner diameter of 100 mm. Find the mass flow rate ṁ.

ρ = 1025 kg/m³v = 1.25 m/sd = 100 mm
ṁ = kg/s
2.Easy
12d1​ = 75 mm, v1​ = 1.5 m/sd2​ = 50 mm

Water flows at 1.5 m/s through the wide section of the pipe, which has a diameter of 75 mm. Find the volume flow rate Q.

d1 = 75 mmd2 = 50 mmv1 = 1.5 m/s
Q = L/s
3.Medium
12d1​ = 80 mm, p1​ = ?d2​ = 40 mm, p2​ = 270 kPa

Water flows at 7 L/s through a horizontal pipe that narrows from 80 mm to 40 mm. The pressure in the narrow section is 270 kPa. Ignoring losses, find the pressure p1 in the wide section.

Q = 7 L/sd1 = 80 mmd2 = 40 mmp2 = 270 kPaρ = 1000 kg/m³
p1 = kPa
4.Medium
12d1​ = 150 mm, p1​ = 310 kPad2​ = 75 mm, p2​ = ?

Water flows through a horizontal pipe that narrows from 150 mm to 75 mm. In the wide section the pressure is 310 kPa and the velocity is 2.5 m/s. Ignoring losses, find the pressure p2 in the narrow section.

d1 = 150 mmd2 = 75 mmp1 = 310 kPav1 = 2.5 m/sρ = 1000 kg/m³
p2 = kPa
5.Hard
12d1​ = 150 mm, p1​ = 160 kPad2​ = 50 mm, p2​ = ?Δz = 9 m

Water flows up through a pipe that narrows from 150 mm to 50 mm while rising 9 m. At section 1 the pressure is 160 kPa and the velocity is 1 m/s. Ignoring losses, find the pressure p2 at section 2.

d1 = 150 mmd2 = 50 mmp1 = 160 kPav1 = 1 m/sΔz = 9 mρ = 1000 kg/m³
p2 = kPa
6.Hard
12d1​ = 75 mm, p1​ = 250 kPad2​ = 25 mm, p2​ = ?Δz = 6 m

Water flows up through a pipe that narrows from 75 mm to 25 mm while rising 6 m. At section 1 the pressure is 250 kPa and the velocity is 0.75 m/s. Ignoring losses, find the pressure p2 at section 2.

d1 = 75 mmd2 = 25 mmp1 = 250 kPav1 = 0.75 m/sΔz = 6 mρ = 1000 kg/m³
p2 = kPa

Answer key

  1. 1. ṁ = 10.06 kg/s
  2. 2. Q = 6.627 L/s
  3. 3. p1 = 284.5 kPa
  4. 4. p2 = 263.1 kPa
  5. 5. p2 = 31.71 kPa
  6. 6. p2 = 168.6 kPa

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