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​ = 150 mm, v1​ = 1 m/sd2​ = 50 mm

Water flows at 1 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 = 1 m/s
Q = L/s
2.Easy
12d1​ = 200 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 200 mm. Find the volume flow rate Q.

d1 = 200 mmd2 = 50 mmv1 = 0.5 m/s
Q = L/s
3.Medium
Q = ?d = 25 mm, Cd​ = 0.64h = 1.5 m

Water drains from a large open tank through a sharp-edged orifice with a diameter of 25 mm. The water level is kept 1.5 m above the orifice and the discharge coefficient is 0.64. Find the flow rate Q. Use g = 9.81 m/s².

d = 25 mmh = 1.5 mCd = 0.64g = 9.81 m/s²
Q = L/s
4.Medium
v = ?p0​pp0​ − p = 7 kPastagnation point

A pitot-static tube in a water pipe reads a difference of 7 kPa between the stagnation pressure and the static pressure. Find the water velocity v at the tip.

p0 − p = 7 kPaρ = 1000 kg/m³
v = m/s
5.Hard
12d1​ = 200 mm, p1​ = 130 kPad2​ = 100 mm, p2​ = ?Δz = 9 m

Water flows up through a pipe that narrows from 200 mm to 100 mm while rising 9 m. At section 1 the pressure is 130 kPa and the velocity is 0.5 m/s. Ignoring losses, find the pressure p2 at section 2.

d1 = 200 mmd2 = 100 mmp1 = 130 kPav1 = 0.5 m/sΔz = 9 mρ = 1000 kg/m³
p2 = kPa
6.Hard
12d1​ = 150 mm, p1​ = 280 kPad2​ = 75 mm, p2​ = ?Δz = 7 m

Water flows up through a pipe that narrows from 150 mm to 75 mm while rising 7 m. At section 1 the pressure is 280 kPa and the velocity is 3 m/s. Ignoring losses, find the pressure p2 at section 2.

d1 = 150 mmd2 = 75 mmp1 = 280 kPav1 = 3 m/sΔz = 7 mρ = 1000 kg/m³
p2 = kPa

Answer key

  1. 1. Q = 17.67 L/s
  2. 2. Q = 15.71 L/s
  3. 3. Q = 1.704 L/s
  4. 4. v = 3.742 m/s
  5. 5. p2 = 39.83 kPa
  6. 6. p2 = 143.8 kPa

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