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 = 20 mmh = 2 m

An open water tank drains through a round opening with a diameter of 20 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 = 20 mm
Q = L/s
2.Easy
vd = 40 mmh = 7 m

An open water tank drains through a round opening with a diameter of 40 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 = 40 mm
Q = L/s
3.Medium
d1​ = 150 mmd2​ = 100 mm12p1​ − p2​ = 8 kPaQ = ?

Water flows through a horizontal venturi meter with an inlet diameter of 150 mm and a throat diameter of 100 mm. The pressure at the inlet is 8 kPa higher than at the throat. Ignoring losses, find the flow rate Q.

d1 = 150 mmd2 = 100 mmp1 − p2 = 8 kPaρ = 1000 kg/m³
Q = L/s
4.Medium
Q = ?d = 20 mm, Cd​ = 0.65h = 2 m

Water drains from a large open tank through a sharp-edged orifice with a diameter of 20 mm. The water level is kept 2 m above the orifice and the discharge coefficient is 0.65. Find the flow rate Q. Use g = 9.81 m/s².

d = 20 mmh = 2 mCd = 0.65g = 9.81 m/s²
Q = L/s
5.Hard
12d1​ = 150 mm, p1​ = 270 kPad2​ = 75 mm, p2​ = ?Δz = 5 m

Water flows up through a pipe that narrows from 150 mm to 75 mm while rising 5 m. At section 1 the pressure is 270 kPa and the velocity is 2.25 m/s. Ignoring losses, find the pressure p2 at section 2.

d1 = 150 mmd2 = 75 mmp1 = 270 kPav1 = 2.25 m/sΔz = 5 mρ = 1000 kg/m³
p2 = kPa
6.Hard
12d1​ = 150 mm, p1​ = 310 kPad2​ = 75 mm, p2​ = ?Δz = 6 m

Water flows up through a pipe that narrows from 150 mm to 75 mm while rising 6 m. At section 1 the pressure is 310 kPa and the velocity is 2.5 m/s. Ignoring losses, find the pressure p2 at section 2.

d1 = 150 mmd2 = 75 mmp1 = 310 kPav1 = 2.5 m/sΔz = 6 mρ = 1000 kg/m³
p2 = kPa

Answer key

  1. 1. Q = 1.968 L/s
  2. 2. Q = 14.73 L/s
  3. 3. Q = 35.07 L/s
  4. 4. Q = 1.279 L/s
  5. 5. p2 = 183 kPa
  6. 6. p2 = 204.3 kPa

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