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​ = 1.5 m/sd2​ = 75 mm, v2​ = ?

Water flows through a pipe that narrows from 100 mm to 75 mm in diameter. The velocity in the wide section is 1.5 m/s. Find the velocity v2 in the narrow section.

d1 = 100 mmd2 = 75 mmv1 = 1.5 m/s
v2 = m/s
2.Easy
12d1​ = 100 mm, v1​ = 0.5 m/sd2​ = 40 mm, v2​ = ?

Water flows through a pipe that narrows from 100 mm to 40 mm in diameter. The velocity in the wide section is 0.5 m/s. Find the velocity v2 in the narrow section.

d1 = 100 mmd2 = 40 mmv1 = 0.5 m/s
v2 = m/s
3.Medium
d1​ = 100 mmd2​ = 50 mm12p1​ − p2​ = 47 kPaQ = ?

Water flows through a horizontal venturi meter with an inlet diameter of 100 mm and a throat diameter of 50 mm. The pressure at the inlet is 47 kPa higher than at the throat. Ignoring losses, find the flow rate Q.

d1 = 100 mmd2 = 50 mmp1 − p2 = 47 kPaρ = 1000 kg/m³
Q = L/s
4.Medium
12d1​ = 75 mm, p1​ = 350 kPad2​ = 50 mm, p2​ = ?

Water flows through a horizontal pipe that narrows from 75 mm to 50 mm. In the wide section the pressure is 350 kPa and the velocity is 0.5 m/s. Ignoring losses, find the pressure p2 in the narrow section.

d1 = 75 mmd2 = 50 mmp1 = 350 kPav1 = 0.5 m/sρ = 1000 kg/m³
p2 = kPa
5.Hard
12d1​ = 75 mm, p1​ = 270 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 270 kPa and the velocity is 1.25 m/s. Ignoring losses, find the pressure p2 at section 2.

d1 = 75 mmd2 = 50 mmp1 = 270 kPav1 = 1.25 m/sΔz = 5 mρ = 1000 kg/m³
p2 = kPa
6.Hard
pair​ = 50 kPav = ?d = 25 mmh = 5 m

A closed water tank has compressed air above the water at a gauge pressure of 50 kPa. Water leaves through an opening with a diameter of 25 mm, 5 m below the water surface, into the open air. Ignoring losses, find the jet velocity v. Use g = 9.81 m/s².

pair = 50 kPa (gauge)h = 5 md = 25 mmρ = 1000 kg/m³g = 9.81 m/s²
v = m/s

Answer key

  1. 1. v2 = 2.667 m/s
  2. 2. v2 = 3.125 m/s
  3. 3. Q = 19.66 L/s
  4. 4. p2 = 349.5 kPa
  5. 5. p2 = 217.8 kPa
  6. 6. v = 14.07 m/s

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