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 = 150 mm, v = 3 m/sṁ = ?

Oil (ρ = 880 kg/m³) flows at 3 m/s through a pipe with an inner diameter of 150 mm. Find the mass flow rate ṁ.

ρ = 880 kg/m³v = 3 m/sd = 150 mm
ṁ = kg/s
2.Easy
12d1​ = 200 mm, v1​ = 1.5 m/sd2​ = 100 mm, v2​ = ?

Water flows through a pipe that narrows from 200 mm to 100 mm in diameter. The velocity in the wide section is 1.5 m/s. Find the velocity v2 in the narrow section.

d1 = 200 mmd2 = 100 mmv1 = 1.5 m/s
v2 = m/s
3.Medium
12d1​ = 150 mm, p1​ = ?d2​ = 75 mm, p2​ = 220 kPa

Water flows at 9 L/s through a horizontal pipe that narrows from 150 mm to 75 mm. The pressure in the narrow section is 220 kPa. Ignoring losses, find the pressure p1 in the wide section.

Q = 9 L/sd1 = 150 mmd2 = 75 mmp2 = 220 kPaρ = 1000 kg/m³
p1 = kPa
4.Medium
12d1​ = 75 mm, p1​ = 290 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 290 kPa and the velocity is 2.5 m/s. Ignoring losses, find the pressure p2 in the narrow section.

d1 = 75 mmd2 = 40 mmp1 = 290 kPav1 = 2.5 m/sρ = 1000 kg/m³
p2 = kPa
5.Hard
12d1​ = 150 mm, p1​ = 140 kPad2​ = 75 mm, p2​ = ?Δz = 5 m

Water flows up through a pipe that narrows from 150 mm to 75 mm while rising 5 m. At section 1 the pressure is 140 kPa and the velocity is 0.75 m/s. Ignoring losses, find the pressure p2 at section 2.

d1 = 150 mmd2 = 75 mmp1 = 140 kPav1 = 0.75 m/sΔz = 5 mρ = 1000 kg/m³
p2 = kPa
6.Hard
12d1​ = 100 mm, p1​ = 190 kPad2​ = 40 mm, p2​ = ?Δz = 7 m

Water flows up through a pipe that narrows from 100 mm to 40 mm while rising 7 m. At section 1 the pressure is 190 kPa and the velocity is 0.75 m/s. Ignoring losses, find the pressure p2 at section 2.

d1 = 100 mmd2 = 40 mmp1 = 190 kPav1 = 0.75 m/sΔz = 7 mρ = 1000 kg/m³
p2 = kPa

Answer key

  1. 1. ṁ = 46.65 kg/s
  2. 2. v2 = 6 m/s
  3. 3. p1 = 221.9 kPa
  4. 4. p2 = 254.5 kPa
  5. 5. p2 = 86.73 kPa
  6. 6. p2 = 110.6 kPa

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