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​ = 100 mm, v1​ = 1.25 m/sd2​ = 40 mm

Water flows at 1.25 m/s through the wide section of the pipe, which has a diameter of 100 mm. Find the volume flow rate Q.

d1 = 100 mmd2 = 40 mmv1 = 1.25 m/s
Q = L/s
2.Easy
vd = 30 mmh = 3.5 m

An open water tank drains through a round opening with a diameter of 30 mm in its side. The free surface is 3.5 m above the opening. Ignoring losses and the contraction of the jet, find the flow rate Q. Use g = 9.81 m/s².

h = 3.5 mg = 9.81 m/s²d = 30 mm
Q = L/s
3.Medium
v = ?p0​pp0​ − p = 900 Pastagnation point

A pitot-static tube in a wind tunnel reads a difference of 900 Pa between the stagnation pressure and the static pressure. The air density is 1.2 kg/m³. Find the air speed v.

p0 − p = 900 Paρ = 1.2 kg/m³
v = m/s
4.Medium
12d1​ = 150 mm, p1​ = 260 kPad2​ = 75 mm, p2​ = ?

Water flows through a horizontal pipe that narrows from 150 mm to 75 mm. In the wide section the pressure is 260 kPa and the velocity is 0.5 m/s. Ignoring losses, find the pressure p2 in the narrow section.

d1 = 150 mmd2 = 75 mmp1 = 260 kPav1 = 0.5 m/sρ = 1000 kg/m³
p2 = kPa
5.Hard
12d1​ = 75 mm, p1​ = 240 kPad2​ = 40 mm, p2​ = ?Δz = 5 m

Water flows up through a pipe that narrows from 75 mm to 40 mm while rising 5 m. At section 1 the pressure is 240 kPa and the velocity is 2.25 m/s. Ignoring losses, find the pressure p2 at section 2.

d1 = 75 mmd2 = 40 mmp1 = 240 kPav1 = 2.25 m/sΔz = 5 mρ = 1000 kg/m³
p2 = kPa
6.Hard
12d1​ = 100 mm, p1​ = 200 kPad2​ = 75 mm, p2​ = ?Δz = 6 m

Water flows up through a pipe that narrows from 100 mm to 75 mm while rising 6 m. At section 1 the pressure is 200 kPa and the velocity is 2.5 m/s. Ignoring losses, find the pressure p2 at section 2.

d1 = 100 mmd2 = 75 mmp1 = 200 kPav1 = 2.5 m/sΔz = 6 mρ = 1000 kg/m³
p2 = kPa

Answer key

  1. 1. Q = 9.817 L/s
  2. 2. Q = 5.858 L/s
  3. 3. v = 38.73 m/s
  4. 4. p2 = 258.1 kPa
  5. 5. p2 = 162.2 kPa
  6. 6. p2 = 134.4 kPa

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