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​ = 75 mm, v1​ = 2.25 m/sd2​ = 50 mm

Water flows at 2.25 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 = 2.25 m/s
Q = L/s
2.Easy
12d = 25 mm, v = 1.75 m/sṁ = ?

Glycerin (ρ = 1260 kg/m³) flows at 1.75 m/s through a pipe with an inner diameter of 25 mm. Find the mass flow rate ṁ.

ρ = 1260 kg/m³v = 1.75 m/sd = 25 mm
ṁ = kg/s
3.Medium
12d1​ = 75 mm, p1​ = 360 kPad2​ = 50 mm, p2​ = ?

Water flows through a horizontal pipe that narrows from 75 mm to 50 mm. In the wide section the pressure is 360 kPa and the velocity is 0.5 m/s. Ignoring losses, find the pressure p2 in the narrow section.

d1 = 75 mmd2 = 50 mmp1 = 360 kPav1 = 0.5 m/sρ = 1000 kg/m³
p2 = kPa
4.Medium
12d1​ = 200 mm, p1​ = 330 kPad2​ = 100 mm, p2​ = ?

Water flows through a horizontal pipe that narrows from 200 mm to 100 mm. In the wide section the pressure is 330 kPa and the velocity is 0.5 m/s. Ignoring losses, find the pressure p2 in the narrow section.

d1 = 200 mmd2 = 100 mmp1 = 330 kPav1 = 0.5 m/sρ = 1000 kg/m³
p2 = kPa
5.Hard
12d1​ = 150 mm, p1​ = 190 kPad2​ = 40 mm, p2​ = ?Δz = 8 m

Water flows up through a pipe that narrows from 150 mm to 40 mm while rising 8 m. At section 1 the pressure is 190 kPa and the velocity is 0.5 m/s. Ignoring losses, find the pressure p2 at section 2.

d1 = 150 mmd2 = 40 mmp1 = 190 kPav1 = 0.5 m/sΔz = 8 mρ = 1000 kg/m³
p2 = kPa
6.Hard
12d1​ = 75 mm, p1​ = 200 kPad2​ = 50 mm, p2​ = ?Δz = 4 m

Water flows up through a pipe that narrows from 75 mm to 50 mm while rising 4 m. At section 1 the pressure is 200 kPa and the velocity is 1.25 m/s. Ignoring losses, find the pressure p2 at section 2.

d1 = 75 mmd2 = 50 mmp1 = 200 kPav1 = 1.25 m/sΔz = 4 mρ = 1000 kg/m³
p2 = kPa

Answer key

  1. 1. Q = 9.94 L/s
  2. 2. ṁ = 1.082 kg/s
  3. 3. p2 = 359.5 kPa
  4. 4. p2 = 328.1 kPa
  5. 5. p2 = 86.93 kPa
  6. 6. p2 = 157.6 kPa

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