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​ = 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
2.Easy
12d = 80 mm, v = 1.75 m/sṁ = ?

Oil (ρ = 880 kg/m³) flows at 1.75 m/s through a pipe with an inner diameter of 80 mm. Find the mass flow rate ṁ.

ρ = 880 kg/m³v = 1.75 m/sd = 80 mm
ṁ = kg/s
3.Medium
d1​ = 250 mmd2​ = 125 mm12p1​ − p2​ = 32 kPaQ = ?

Water flows through a horizontal venturi meter with an inlet diameter of 250 mm and a throat diameter of 125 mm. The pressure at the inlet is 32 kPa higher than at the throat. Ignoring losses, find the flow rate Q.

d1 = 250 mmd2 = 125 mmp1 − p2 = 32 kPaρ = 1000 kg/m³
Q = L/s
4.Medium
12d1​ = 75 mm, p1​ = 240 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 240 kPa and the velocity is 0.75 m/s. Ignoring losses, find the pressure p2 in the narrow section.

d1 = 75 mmd2 = 40 mmp1 = 240 kPav1 = 0.75 m/sρ = 1000 kg/m³
p2 = kPa
5.Hard
12d1​ = 75 mm, p1​ = 260 kPad2​ = 25 mm, p2​ = ?Δz = 8 m

Water flows up through a pipe that narrows from 75 mm to 25 mm while rising 8 m. At section 1 the pressure is 260 kPa and the velocity is 1 m/s. Ignoring losses, find the pressure p2 at section 2.

d1 = 75 mmd2 = 25 mmp1 = 260 kPav1 = 1 m/sΔz = 8 mρ = 1000 kg/m³
p2 = kPa
6.Hard
12d1​ = 100 mm, p1​ = 100 kPad2​ = 75 mm, p2​ = ?Δz = 7 m

Water flows up through a pipe that narrows from 100 mm to 75 mm while rising 7 m. At section 1 the pressure is 100 kPa and the velocity is 3 m/s. Ignoring losses, find the pressure p2 at section 2.

d1 = 100 mmd2 = 75 mmp1 = 100 kPav1 = 3 m/sΔz = 7 mρ = 1000 kg/m³
p2 = kPa

Answer key

  1. 1. v2 = 9 m/s
  2. 2. ṁ = 7.741 kg/s
  3. 3. Q = 101.4 L/s
  4. 4. p2 = 236.8 kPa
  5. 5. p2 = 141.5 kPa
  6. 6. p2 = 21.61 kPa

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