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 = 3.75 m/sṁ = ?

Glycerin (ρ = 1260 kg/m³) flows at 3.75 m/s through a pipe with an inner diameter of 100 mm. Find the mass flow rate ṁ.

ρ = 1260 kg/m³v = 3.75 m/sd = 100 mm
ṁ = kg/s
2.Easy
12d1​ = 150 mm, v1​ = 2.25 m/sd2​ = 75 mm

Water flows at 2.25 m/s through the wide section of the pipe, which has a diameter of 150 mm. Find the volume flow rate Q.

d1 = 150 mmd2 = 75 mmv1 = 2.25 m/s
Q = L/s
3.Medium
12d1​ = 100 mm, p1​ = 140 kPad2​ = 40 mm, p2​ = ?

Water flows through a horizontal pipe that narrows from 100 mm to 40 mm. In the wide section the pressure is 140 kPa and the velocity is 1.5 m/s. Ignoring losses, find the pressure p2 in the narrow section.

d1 = 100 mmd2 = 40 mmp1 = 140 kPav1 = 1.5 m/sρ = 1000 kg/m³
p2 = kPa
4.Medium
d1​ = 100 mmd2​ = 50 mm12p1​ − p2​ = 5 kPaQ = ?

Water flows through a horizontal venturi meter with an inlet diameter of 100 mm and a throat diameter of 50 mm. The pressure at the inlet is 5 kPa higher than at the throat. Ignoring losses, find the flow rate Q.

d1 = 100 mmd2 = 50 mmp1 − p2 = 5 kPaρ = 1000 kg/m³
Q = L/s
5.Hard
12d1​ = 100 mm, p1​ = 140 kPad2​ = 40 mm, p2​ = ?Δz = 10 m

Water flows up through a pipe that narrows from 100 mm to 40 mm while rising 10 m. At section 1 the pressure is 140 kPa and the velocity is 0.5 m/s. Ignoring losses, find the pressure p2 at section 2.

d1 = 100 mmd2 = 40 mmp1 = 140 kPav1 = 0.5 m/sΔz = 10 mρ = 1000 kg/m³
p2 = kPa
6.Hard
12d1​ = 75 mm, p1​ = 170 kPad2​ = 50 mm, p2​ = ?Δz = 9 m

Water flows up through a pipe that narrows from 75 mm to 50 mm while rising 9 m. At section 1 the pressure is 170 kPa and the velocity is 2.25 m/s. Ignoring losses, find the pressure p2 at section 2.

d1 = 75 mmd2 = 50 mmp1 = 170 kPav1 = 2.25 m/sΔz = 9 mρ = 1000 kg/m³
p2 = kPa

Answer key

  1. 1. ṁ = 37.11 kg/s
  2. 2. Q = 39.76 L/s
  3. 3. p2 = 97.18 kPa
  4. 4. Q = 6.413 L/s
  5. 5. p2 = 37.14 kPa
  6. 6. p2 = 71.43 kPa

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