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 m/sṁ = ?

Water (ρ = 1000 kg/m³) flows at 1 m/s through a pipe with an inner diameter of 100 mm. Find the mass flow rate ṁ.

ρ = 1000 kg/m³v = 1 m/sd = 100 mm
ṁ = kg/s
2.Easy
12d = 150 mm, v = 0.75 m/sṁ = ?

Water (ρ = 1000 kg/m³) flows at 0.75 m/s through a pipe with an inner diameter of 150 mm. Find the mass flow rate ṁ.

ρ = 1000 kg/m³v = 0.75 m/sd = 150 mm
ṁ = kg/s
3.Medium
12d1​ = 100 mm, p1​ = ?d2​ = 75 mm, p2​ = 220 kPa

Water flows at 40 L/s through a horizontal pipe that narrows from 100 mm to 75 mm. The pressure in the narrow section is 220 kPa. Ignoring losses, find the pressure p1 in the wide section.

Q = 40 L/sd1 = 100 mmd2 = 75 mmp2 = 220 kPaρ = 1000 kg/m³
p1 = kPa
4.Medium
d1​ = 150 mmd2​ = 100 mm12p1​ − p2​ = 18 kPaQ = ?

Water flows through a horizontal venturi meter with an inlet diameter of 150 mm and a throat diameter of 100 mm. The pressure at the inlet is 18 kPa higher than at the throat. Ignoring losses, find the flow rate Q.

d1 = 150 mmd2 = 100 mmp1 − p2 = 18 kPaρ = 1000 kg/m³
Q = L/s
5.Hard
12d1​ = 100 mm, p1​ = 280 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 280 kPa and the velocity is 2.25 m/s. Ignoring losses, find the pressure p2 at section 2.

d1 = 100 mmd2 = 50 mmp1 = 280 kPav1 = 2.25 m/sΔz = 7 mρ = 1000 kg/m³
p2 = kPa
6.Hard
12d1​ = 75 mm, p1​ = 350 kPad2​ = 25 mm, p2​ = ?Δz = 10 m

Water flows up through a pipe that narrows from 75 mm to 25 mm while rising 10 m. At section 1 the pressure is 350 kPa and the velocity is 1 m/s. Ignoring losses, find the pressure p2 at section 2.

d1 = 75 mmd2 = 25 mmp1 = 350 kPav1 = 1 m/sΔz = 10 mρ = 1000 kg/m³
p2 = kPa

Answer key

  1. 1. ṁ = 7.854 kg/s
  2. 2. ṁ = 13.25 kg/s
  3. 3. p1 = 248 kPa
  4. 4. Q = 52.6 L/s
  5. 5. p2 = 173.4 kPa
  6. 6. p2 = 211.9 kPa

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