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 = 15 mmh = 7 m

An open water tank drains through a round opening with a diameter of 15 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 = 15 mm
Q = L/s
2.Easy
vd = 15 mmh = 8 m

An open water tank drains through a round opening with a diameter of 15 mm in its side. The free surface is 8 m above the opening. Ignoring losses and the contraction of the jet, find the flow rate Q. Use g = 9.81 m/s².

h = 8 mg = 9.81 m/s²d = 15 mm
Q = L/s
3.Medium
12d1​ = 100 mm, p1​ = 170 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 170 kPa and the velocity is 2.75 m/s. Ignoring losses, find the pressure p2 in the narrow section.

d1 = 100 mmd2 = 50 mmp1 = 170 kPav1 = 2.75 m/sρ = 1000 kg/m³
p2 = kPa
4.Medium
Q = ?d = 50 mm, Cd​ = 0.61h = 3 m

Water drains from a large open tank through a sharp-edged orifice with a diameter of 50 mm. The water level is kept 3 m above the orifice and the discharge coefficient is 0.61. Find the flow rate Q. Use g = 9.81 m/s².

d = 50 mmh = 3 mCd = 0.61g = 9.81 m/s²
Q = L/s
5.Hard
12d1​ = 150 mm, p1​ = 260 kPad2​ = 100 mm, p2​ = ?Δz = 7 m

Water flows up through a pipe that narrows from 150 mm to 100 mm while rising 7 m. At section 1 the pressure is 260 kPa and the velocity is 1.25 m/s. Ignoring losses, find the pressure p2 at section 2.

d1 = 150 mmd2 = 100 mmp1 = 260 kPav1 = 1.25 m/sΔz = 7 mρ = 1000 kg/m³
p2 = kPa
6.Hard
12d1​ = 75 mm, p1​ = 160 kPad2​ = 40 mm, p2​ = ?Δz = 5 m

Water flows up through a pipe that narrows from 75 mm to 40 mm while rising 5 m. At section 1 the pressure is 160 kPa and the velocity is 3 m/s. Ignoring losses, find the pressure p2 at section 2.

d1 = 75 mmd2 = 40 mmp1 = 160 kPav1 = 3 m/sΔz = 5 mρ = 1000 kg/m³
p2 = kPa

Answer key

  1. 1. Q = 2.071 L/s
  2. 2. Q = 2.214 L/s
  3. 3. p2 = 113.3 kPa
  4. 4. Q = 9.189 L/s
  5. 5. p2 = 188.2 kPa
  6. 6. p2 = 59.83 kPa

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