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​ = 0.75 m/sd2​ = 50 mm

Water flows at 0.75 m/s through the wide section of the pipe, which has a diameter of 75 mm. Find the volume flow rate Q.

d1 = 75 mmd2 = 50 mmv1 = 0.75 m/s
Q = L/s
2.Easy
12Q = 9 L/sv = 2 m/s, d = ?

A water line must carry 9 L/s. To limit noise and wear, the mean velocity should be 2 m/s. Find the inner pipe diameter d needed.

Q = 9 L/sv = 2 m/s
d = mm
3.Medium
v = ?p0​pp0​ − p = 9 kPastagnation point

A pitot-static tube in a water pipe reads a difference of 9 kPa between the stagnation pressure and the static pressure. Find the water velocity v at the tip.

p0 − p = 9 kPaρ = 1000 kg/m³
v = m/s
4.Medium
d1​ = 150 mmd2​ = 75 mm12p1​ − p2​ = 38 kPaQ = ?

Water flows through a horizontal venturi meter with an inlet diameter of 150 mm and a throat diameter of 75 mm. The pressure at the inlet is 38 kPa higher than at the throat. Ignoring losses, find the flow rate Q.

d1 = 150 mmd2 = 75 mmp1 − p2 = 38 kPaρ = 1000 kg/m³
Q = L/s
5.Hard
12d1​ = 100 mm, p1​ = 260 kPad2​ = 40 mm, p2​ = ?Δz = 5 m

Water flows up through a pipe that narrows from 100 mm to 40 mm while rising 5 m. At section 1 the pressure is 260 kPa and the velocity is 1.75 m/s. Ignoring losses, find the pressure p2 at section 2.

d1 = 100 mmd2 = 40 mmp1 = 260 kPav1 = 1.75 m/sΔz = 5 mρ = 1000 kg/m³
p2 = kPa
6.Hard
12d1​ = 200 mm, p1​ = 230 kPad2​ = 100 mm, p2​ = ?Δz = 1 m

Water flows up through a pipe that narrows from 200 mm to 100 mm while rising 1 m. At section 1 the pressure is 230 kPa and the velocity is 1.75 m/s. Ignoring losses, find the pressure p2 at section 2.

d1 = 200 mmd2 = 100 mmp1 = 230 kPav1 = 1.75 m/sΔz = 1 mρ = 1000 kg/m³
p2 = kPa

Answer key

  1. 1. Q = 3.313 L/s
  2. 2. d = 75.69 mm
  3. 3. v = 4.243 m/s
  4. 4. Q = 39.78 L/s
  5. 5. p2 = 152.7 kPa
  6. 6. p2 = 197.2 kPa

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