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​ = 1.75 m/sd2​ = 40 mm, v2​ = ?

Water flows through a pipe that narrows from 75 mm to 40 mm in diameter. The velocity in the wide section is 1.75 m/s. Find the velocity v2 in the narrow section.

d1 = 75 mmd2 = 40 mmv1 = 1.75 m/s
v2 = m/s
2.Easy
vd = 20 mmh = 7 m

An open water tank drains through a round opening with a diameter of 20 mm in its side. The free surface is 7 m above the opening. Ignoring losses and the contraction of the jet, find the flow rate Q. Use g = 9.81 m/s².

h = 7 mg = 9.81 m/s²d = 20 mm
Q = L/s
3.Medium
12d1​ = 150 mm, p1​ = ?d2​ = 100 mm, p2​ = 70 kPa

Water flows at 11 L/s through a horizontal pipe that narrows from 150 mm to 100 mm. The pressure in the narrow section is 70 kPa. Ignoring losses, find the pressure p1 in the wide section.

Q = 11 L/sd1 = 150 mmd2 = 100 mmp2 = 70 kPaρ = 1000 kg/m³
p1 = kPa
4.Medium
v = ?p0​pp0​ − p = 7 kPastagnation point

A pitot-static tube in a water pipe reads a difference of 7 kPa between the stagnation pressure and the static pressure. Find the water velocity v at the tip.

p0 − p = 7 kPaρ = 1000 kg/m³
v = m/s
5.Hard
12d1​ = 200 mm, p1​ = 220 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 220 kPa and the velocity is 1 m/s. Ignoring losses, find the pressure p2 at section 2.

d1 = 200 mmd2 = 100 mmp1 = 220 kPav1 = 1 m/sΔz = 1 mρ = 1000 kg/m³
p2 = kPa
6.Hard
12d1​ = 100 mm, p1​ = 400 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 400 kPa and the velocity is 3 m/s. Ignoring losses, find the pressure p2 at section 2.

d1 = 100 mmd2 = 50 mmp1 = 400 kPav1 = 3 m/sΔz = 1 mρ = 1000 kg/m³
p2 = kPa

Answer key

  1. 1. v2 = 6.152 m/s
  2. 2. Q = 3.682 L/s
  3. 3. p1 = 70.79 kPa
  4. 4. v = 3.742 m/s
  5. 5. p2 = 202.7 kPa
  6. 6. p2 = 322.7 kPa

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