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 = 30 mmh = 5.5 m

An open water tank drains through a round opening with a diameter of 30 mm in its side. The free surface is 5.5 m above the opening. Ignoring losses and the contraction of the jet, find the flow rate Q. Use g = 9.81 m/s².

h = 5.5 mg = 9.81 m/s²d = 30 mm
Q = L/s
2.Easy
vd = 20 mmh = 6.5 m

An open water tank drains through a round opening with a diameter of 20 mm in its side. The free surface is 6.5 m above the opening. Ignoring losses and the contraction of the jet, find the flow rate Q. Use g = 9.81 m/s².

h = 6.5 mg = 9.81 m/s²d = 20 mm
Q = L/s
3.Medium
12d1​ = 75 mm, p1​ = 120 kPad2​ = 50 mm, p2​ = ?

Water flows through a horizontal pipe that narrows from 75 mm to 50 mm. In the wide section the pressure is 120 kPa and the velocity is 2.25 m/s. Ignoring losses, find the pressure p2 in the narrow section.

d1 = 75 mmd2 = 50 mmp1 = 120 kPav1 = 2.25 m/sρ = 1000 kg/m³
p2 = kPa
4.Medium
d1​ = 200 mmd2​ = 100 mm12p1​ − p2​ = 49 kPaQ = ?

Water flows through a horizontal venturi meter with an inlet diameter of 200 mm and a throat diameter of 100 mm. The pressure at the inlet is 49 kPa higher than at the throat. Ignoring losses, find the flow rate Q.

d1 = 200 mmd2 = 100 mmp1 − p2 = 49 kPaρ = 1000 kg/m³
Q = L/s
5.Hard
pair​ = 170 kPaQ = ?d = 20 mmh = 4.5 m

A closed water tank has compressed air above the water at a gauge pressure of 170 kPa. Water leaves through an opening with a diameter of 20 mm, 4.5 m below the water surface, into the open air. Ignoring losses, find the flow rate Q. Use g = 9.81 m/s².

pair = 170 kPa (gauge)h = 4.5 md = 20 mmρ = 1000 kg/m³g = 9.81 m/s²
Q = L/s
6.Hard
12d1​ = 200 mm, p1​ = 390 kPad2​ = 100 mm, p2​ = ?Δz = 10 m

Water flows up through a pipe that narrows from 200 mm to 100 mm while rising 10 m. At section 1 the pressure is 390 kPa and the velocity is 1.25 m/s. Ignoring losses, find the pressure p2 at section 2.

d1 = 200 mmd2 = 100 mmp1 = 390 kPav1 = 1.25 m/sΔz = 10 mρ = 1000 kg/m³
p2 = kPa

Answer key

  1. 1. Q = 7.343 L/s
  2. 2. Q = 3.548 L/s
  3. 3. p2 = 109.7 kPa
  4. 4. Q = 80.3 L/s
  5. 5. Q = 6.502 L/s
  6. 6. p2 = 280.2 kPa

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