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​ = 100 mm, v1​ = 2 m/sd2​ = 50 mm, v2​ = ?

Water flows through a pipe that narrows from 100 mm to 50 mm in diameter. The velocity in the wide section is 2 m/s. Find the velocity v2 in the narrow section.

d1 = 100 mmd2 = 50 mmv1 = 2 m/s
v2 = m/s
2.Easy
v = ?h = 1.5 m

An open water tank drains through a small opening in its side. The free surface is 1.5 m above the opening. Ignoring losses, find the jet velocity v at the opening. Use g = 9.81 m/s².

h = 1.5 mg = 9.81 m/s²
v = m/s
3.Medium
12d1​ = 75 mm, p1​ = 380 kPad2​ = 40 mm, p2​ = ?

Water flows through a horizontal pipe that narrows from 75 mm to 40 mm. In the wide section the pressure is 380 kPa and the velocity is 1.25 m/s. Ignoring losses, find the pressure p2 in the narrow section.

d1 = 75 mmd2 = 40 mmp1 = 380 kPav1 = 1.25 m/sρ = 1000 kg/m³
p2 = kPa
4.Medium
Q = ?d = 30 mm, Cd​ = 0.64h = 4.5 m

Water drains from a large open tank through a sharp-edged orifice with a diameter of 30 mm. The water level is kept 4.5 m above the orifice and the discharge coefficient is 0.64. Find the flow rate Q. Use g = 9.81 m/s².

d = 30 mmh = 4.5 mCd = 0.64g = 9.81 m/s²
Q = L/s
5.Hard
12d1​ = 150 mm, p1​ = 390 kPad2​ = 50 mm, p2​ = ?Δz = 10 m

Water flows up through a pipe that narrows from 150 mm to 50 mm while rising 10 m. At section 1 the pressure is 390 kPa and the velocity is 0.5 m/s. Ignoring losses, find the pressure p2 at section 2.

d1 = 150 mmd2 = 50 mmp1 = 390 kPav1 = 0.5 m/sΔz = 10 mρ = 1000 kg/m³
p2 = kPa
6.Hard
12d1​ = 75 mm, p1​ = 180 kPad2​ = 40 mm, p2​ = ?Δz = 1 m

Water flows up through a pipe that narrows from 75 mm to 40 mm while rising 1 m. At section 1 the pressure is 180 kPa and the velocity is 2 m/s. Ignoring losses, find the pressure p2 at section 2.

d1 = 75 mmd2 = 40 mmp1 = 180 kPav1 = 2 m/sΔz = 1 mρ = 1000 kg/m³
p2 = kPa

Answer key

  1. 1. v2 = 8 m/s
  2. 2. v = 5.425 m/s
  3. 3. p2 = 371.1 kPa
  4. 4. Q = 4.251 L/s
  5. 5. p2 = 281.9 kPa
  6. 6. p2 = 147.5 kPa

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