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
12Q = 39 L/sv = 3 m/s, d = ?

A water line must carry 39 L/s. To limit noise and wear, the mean velocity should be 3 m/s. Find the inner pipe diameter d needed.

Q = 39 L/sv = 3 m/s
d = mm
2.Easy
12d1​ = 75 mm, v1​ = 0.5 m/sd2​ = 50 mm, v2​ = ?

Water flows through a pipe that narrows from 75 mm to 50 mm in diameter. The velocity in the wide section is 0.5 m/s. Find the velocity v2 in the narrow section.

d1 = 75 mmd2 = 50 mmv1 = 0.5 m/s
v2 = m/s
3.Medium
d1​ = 80 mmd2​ = 40 mm12p1​ − p2​ = 7 kPaQ = ?

Water flows through a horizontal venturi meter with an inlet diameter of 80 mm and a throat diameter of 40 mm. The pressure at the inlet is 7 kPa higher than at the throat. Ignoring losses, find the flow rate Q.

d1 = 80 mmd2 = 40 mmp1 − p2 = 7 kPaρ = 1000 kg/m³
Q = L/s
4.Medium
d1​ = 300 mmd2​ = 150 mm12p1​ − p2​ = 11 kPaQ = ?

Water flows through a horizontal venturi meter with an inlet diameter of 300 mm and a throat diameter of 150 mm. The pressure at the inlet is 11 kPa higher than at the throat. Ignoring losses, find the flow rate Q.

d1 = 300 mmd2 = 150 mmp1 − p2 = 11 kPaρ = 1000 kg/m³
Q = L/s
5.Hard
pair​ = 200 kPaQ = ?d = 50 mmh = 3 m

A closed water tank has compressed air above the water at a gauge pressure of 200 kPa. Water leaves through an opening with a diameter of 50 mm, 3 m below the water surface, into the open air. Ignoring losses, find the flow rate Q. Use g = 9.81 m/s².

pair = 200 kPa (gauge)h = 3 md = 50 mmρ = 1000 kg/m³g = 9.81 m/s²
Q = L/s
6.Hard
12d1​ = 150 mm, p1​ = 150 kPad2​ = 75 mm, p2​ = ?Δz = 5 m

Water flows up through a pipe that narrows from 150 mm to 75 mm while rising 5 m. At section 1 the pressure is 150 kPa and the velocity is 0.75 m/s. Ignoring losses, find the pressure p2 at section 2.

d1 = 150 mmd2 = 75 mmp1 = 150 kPav1 = 0.75 m/sΔz = 5 mρ = 1000 kg/m³
p2 = kPa

Answer key

  1. 1. d = 128.7 mm
  2. 2. v2 = 1.125 m/s
  3. 3. Q = 4.856 L/s
  4. 4. Q = 85.6 L/s
  5. 5. Q = 42.06 L/s
  6. 6. p2 = 96.73 kPa

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