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​ = 200 mm, v1​ = 2 m/sd2​ = 75 mm

Water flows at 2 m/s through the wide section of the pipe, which has a diameter of 200 mm. Find the volume flow rate Q.

d1 = 200 mmd2 = 75 mmv1 = 2 m/s
Q = L/s
2.Easy
12d1​ = 150 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 150 mm. Find the volume flow rate Q.

d1 = 150 mmd2 = 50 mmv1 = 0.5 m/s
Q = L/s
3.Medium
12d1​ = 200 mm, p1​ = 150 kPad2​ = 100 mm, p2​ = ?

Water flows through a horizontal pipe that narrows from 200 mm to 100 mm. In the wide section the pressure is 150 kPa and the velocity is 1.25 m/s. Ignoring losses, find the pressure p2 in the narrow section.

d1 = 200 mmd2 = 100 mmp1 = 150 kPav1 = 1.25 m/sρ = 1000 kg/m³
p2 = kPa
4.Medium
12d1​ = 100 mm, p1​ = 370 kPad2​ = 50 mm, p2​ = ?

Water flows through a horizontal pipe that narrows from 100 mm to 50 mm. In the wide section the pressure is 370 kPa and the velocity is 1.5 m/s. Ignoring losses, find the pressure p2 in the narrow section.

d1 = 100 mmd2 = 50 mmp1 = 370 kPav1 = 1.5 m/sρ = 1000 kg/m³
p2 = kPa
5.Hard
pair​ = 80 kPaQ = ?d = 20 mmh = 1.5 m

A closed water tank has compressed air above the water at a gauge pressure of 80 kPa. Water leaves through an opening with a diameter of 20 mm, 1.5 m below the water surface, into the open air. Ignoring losses, find the flow rate Q. Use g = 9.81 m/s².

pair = 80 kPa (gauge)h = 1.5 md = 20 mmρ = 1000 kg/m³g = 9.81 m/s²
Q = L/s
6.Hard
12d1​ = 100 mm, p1​ = 220 kPad2​ = 50 mm, p2​ = ?Δz = 9 m

Water flows up through a pipe that narrows from 100 mm to 50 mm while rising 9 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 = 100 mmd2 = 50 mmp1 = 220 kPav1 = 1 m/sΔz = 9 mρ = 1000 kg/m³
p2 = kPa

Answer key

  1. 1. Q = 62.83 L/s
  2. 2. Q = 8.836 L/s
  3. 3. p2 = 138.3 kPa
  4. 4. p2 = 353.1 kPa
  5. 5. Q = 4.324 L/s
  6. 6. p2 = 124.2 kPa

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