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​ = 3 m/sd2​ = 100 mm

Water flows at 3 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 = 100 mmv1 = 3 m/s
Q = L/s
2.Easy
12d1​ = 75 mm, v1​ = 1.25 m/sd2​ = 50 mm

Water flows at 1.25 m/s through the wide section of the pipe, which has a diameter of 75 mm. Find the volume flow rate Q.

d1 = 75 mmd2 = 50 mmv1 = 1.25 m/s
Q = L/s
3.Medium
Q = ?d = 40 mm, Cd​ = 0.63h = 2 m

Water drains from a large open tank through a sharp-edged orifice with a diameter of 40 mm. The water level is kept 2 m above the orifice and the discharge coefficient is 0.63. Find the flow rate Q. Use g = 9.81 m/s².

d = 40 mmh = 2 mCd = 0.63g = 9.81 m/s²
Q = L/s
4.Medium
d1​ = 200 mmd2​ = 150 mm12p1​ − p2​ = 12 kPaQ = ?

Water flows through a horizontal venturi meter with an inlet diameter of 200 mm and a throat diameter of 150 mm. The pressure at the inlet is 12 kPa higher than at the throat. Ignoring losses, find the flow rate Q.

d1 = 200 mmd2 = 150 mmp1 − p2 = 12 kPaρ = 1000 kg/m³
Q = L/s
5.Hard
12d1​ = 200 mm, p1​ = 250 kPad2​ = 50 mm, p2​ = ?Δz = 2 m

Water flows up through a pipe that narrows from 200 mm to 50 mm while rising 2 m. At section 1 the pressure is 250 kPa and the velocity is 0.5 m/s. Ignoring losses, find the pressure p2 at section 2.

d1 = 200 mmd2 = 50 mmp1 = 250 kPav1 = 0.5 m/sΔz = 2 mρ = 1000 kg/m³
p2 = kPa
6.Hard
12d1​ = 75 mm, p1​ = 150 kPad2​ = 50 mm, p2​ = ?Δz = 5 m

Water flows up through a pipe that narrows from 75 mm to 50 mm while rising 5 m. At section 1 the pressure is 150 kPa and the velocity is 2 m/s. Ignoring losses, find the pressure p2 at section 2.

d1 = 75 mmd2 = 50 mmp1 = 150 kPav1 = 2 m/sΔz = 5 mρ = 1000 kg/m³
p2 = kPa

Answer key

  1. 1. Q = 94.25 L/s
  2. 2. Q = 5.522 L/s
  3. 3. Q = 4.959 L/s
  4. 4. Q = 104.7 L/s
  5. 5. p2 = 198.5 kPa
  6. 6. p2 = 92.83 kPa

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