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
vd = 40 mmh = 2 m

An open water tank drains through a round opening with a diameter of 40 mm in its side. The free surface is 2 m above the opening. Ignoring losses and the contraction of the jet, find the flow rate Q. Use g = 9.81 m/s².

h = 2 mg = 9.81 m/s²d = 40 mm
Q = L/s
2.Easy
12d1​ = 100 mm, v1​ = 0.5 m/sd2​ = 50 mm

Water flows at 0.5 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 = 50 mmv1 = 0.5 m/s
Q = L/s
3.Medium
12d1​ = 150 mm, p1​ = 170 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 170 kPa and the velocity is 1.25 m/s. Ignoring losses, find the pressure p2 in the narrow section.

d1 = 150 mmd2 = 75 mmp1 = 170 kPav1 = 1.25 m/sρ = 1000 kg/m³
p2 = kPa
4.Medium
12d1​ = 200 mm, p1​ = 340 kPad2​ = 75 mm, p2​ = ?

Water flows through a horizontal pipe that narrows from 200 mm to 75 mm. In the wide section the pressure is 340 kPa and the velocity is 1.25 m/s. Ignoring losses, find the pressure p2 in the narrow section.

d1 = 200 mmd2 = 75 mmp1 = 340 kPav1 = 1.25 m/sρ = 1000 kg/m³
p2 = kPa
5.Hard
12d1​ = 200 mm, p1​ = 370 kPad2​ = 100 mm, p2​ = ?Δz = 7 m

Water flows up through a pipe that narrows from 200 mm to 100 mm while rising 7 m. At section 1 the pressure is 370 kPa and the velocity is 0.75 m/s. Ignoring losses, find the pressure p2 at section 2.

d1 = 200 mmd2 = 100 mmp1 = 370 kPav1 = 0.75 m/sΔz = 7 mρ = 1000 kg/m³
p2 = kPa
6.Hard
12d1​ = 200 mm, p1​ = 180 kPad2​ = 100 mm, p2​ = ?Δz = 7 m

Water flows up through a pipe that narrows from 200 mm to 100 mm while rising 7 m. At section 1 the pressure is 180 kPa and the velocity is 1.5 m/s. Ignoring losses, find the pressure p2 at section 2.

d1 = 200 mmd2 = 100 mmp1 = 180 kPav1 = 1.5 m/sΔz = 7 mρ = 1000 kg/m³
p2 = kPa

Answer key

  1. 1. Q = 7.872 L/s
  2. 2. Q = 3.927 L/s
  3. 3. p2 = 158.3 kPa
  4. 4. p2 = 301.3 kPa
  5. 5. p2 = 297.1 kPa
  6. 6. p2 = 94.45 kPa

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