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 = 25 mm, v = 2.75 m/sṁ = ?

Seawater (ρ = 1025 kg/m³) flows at 2.75 m/s through a pipe with an inner diameter of 25 mm. Find the mass flow rate ṁ.

ρ = 1025 kg/m³v = 2.75 m/sd = 25 mm
ṁ = kg/s
2.Easy
12d1​ = 150 mm, v1​ = 0.75 m/sd2​ = 40 mm, v2​ = ?

Water flows through a pipe that narrows from 150 mm to 40 mm in diameter. The velocity in the wide section is 0.75 m/s. Find the velocity v2 in the narrow section.

d1 = 150 mmd2 = 40 mmv1 = 0.75 m/s
v2 = m/s
3.Medium
12d1​ = 75 mm, p1​ = 180 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 180 kPa and the velocity is 0.5 m/s. Ignoring losses, find the pressure p2 in the narrow section.

d1 = 75 mmd2 = 40 mmp1 = 180 kPav1 = 0.5 m/sρ = 1000 kg/m³
p2 = kPa
4.Medium
d1​ = 100 mmd2​ = 60 mm12p1​ − p2​ = 7 kPaQ = ?

Water flows through a horizontal venturi meter with an inlet diameter of 100 mm and a throat diameter of 60 mm. The pressure at the inlet is 7 kPa higher than at the throat. Ignoring losses, find the flow rate Q.

d1 = 100 mmd2 = 60 mmp1 − p2 = 7 kPaρ = 1000 kg/m³
Q = L/s
5.Hard
12d1​ = 100 mm, p1​ = 240 kPad2​ = 50 mm, p2​ = ?Δz = 1 m

Water flows up through a pipe that narrows from 100 mm to 50 mm while rising 1 m. At section 1 the pressure is 240 kPa and the velocity is 0.75 m/s. Ignoring losses, find the pressure p2 at section 2.

d1 = 100 mmd2 = 50 mmp1 = 240 kPav1 = 0.75 m/sΔz = 1 mρ = 1000 kg/m³
p2 = kPa
6.Hard
12d1​ = 200 mm, p1​ = 340 kPad2​ = 100 mm, p2​ = ?Δz = 7 m

Water flows up through a pipe that narrows from 200 mm to 100 mm while rising 7 m. At section 1 the pressure is 340 kPa and the velocity is 1.25 m/s. Ignoring losses, find the pressure p2 at section 2.

d1 = 200 mmd2 = 100 mmp1 = 340 kPav1 = 1.25 m/sΔz = 7 mρ = 1000 kg/m³
p2 = kPa

Answer key

  1. 1. ṁ = 1.384 kg/s
  2. 2. v2 = 10.55 m/s
  3. 3. p2 = 178.6 kPa
  4. 4. Q = 11.34 L/s
  5. 5. p2 = 226 kPa
  6. 6. p2 = 259.6 kPa

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