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 = 50 mm, v = 1.25 m/sṁ = ?

Glycerin (ρ = 1260 kg/m³) flows at 1.25 m/s through a pipe with an inner diameter of 50 mm. Find the mass flow rate ṁ.

ρ = 1260 kg/m³v = 1.25 m/sd = 50 mm
ṁ = kg/s
2.Easy
12d1​ = 75 mm, v1​ = 1 m/sd2​ = 25 mm, v2​ = ?

Water flows through a pipe that narrows from 75 mm to 25 mm in diameter. The velocity in the wide section is 1 m/s. Find the velocity v2 in the narrow section.

d1 = 75 mmd2 = 25 mmv1 = 1 m/s
v2 = m/s
3.Medium
12d1​ = 200 mm, p1​ = 380 kPad2​ = 75 mm, p2​ = ?

Water flows through a horizontal pipe that narrows from 200 mm to 75 mm. In the wide section the pressure is 380 kPa and the velocity is 1.25 m/s. Ignoring losses, find the pressure p2 in the narrow section.

d1 = 200 mmd2 = 75 mmp1 = 380 kPav1 = 1.25 m/sρ = 1000 kg/m³
p2 = kPa
4.Medium
12d1​ = 75 mm, p1​ = 300 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 300 kPa and the velocity is 3 m/s. Ignoring losses, find the pressure p2 in the narrow section.

d1 = 75 mmd2 = 40 mmp1 = 300 kPav1 = 3 m/sρ = 1000 kg/m³
p2 = kPa
5.Hard
12d1​ = 75 mm, p1​ = 360 kPad2​ = 40 mm, p2​ = ?Δz = 6 m

Water flows up through a pipe that narrows from 75 mm to 40 mm while rising 6 m. At section 1 the pressure is 360 kPa and the velocity is 2.75 m/s. Ignoring losses, find the pressure p2 at section 2.

d1 = 75 mmd2 = 40 mmp1 = 360 kPav1 = 2.75 m/sΔz = 6 mρ = 1000 kg/m³
p2 = kPa
6.Hard
12d1​ = 100 mm, p1​ = 200 kPad2​ = 50 mm, p2​ = ?Δz = 7 m

Water flows up through a pipe that narrows from 100 mm to 50 mm while rising 7 m. At section 1 the pressure is 200 kPa and the velocity is 1 m/s. Ignoring losses, find the pressure p2 at section 2.

d1 = 100 mmd2 = 50 mmp1 = 200 kPav1 = 1 m/sΔz = 7 mρ = 1000 kg/m³
p2 = kPa

Answer key

  1. 1. ṁ = 3.093 kg/s
  2. 2. v2 = 9 m/s
  3. 3. p2 = 341.3 kPa
  4. 4. p2 = 248.9 kPa
  5. 5. p2 = 258.2 kPa
  6. 6. p2 = 123.8 kPa

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