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
12d = 80 mm, v = 3 m/sṁ = ?

Seawater (ρ = 1025 kg/m³) flows at 3 m/s through a pipe with an inner diameter of 80 mm. Find the mass flow rate ṁ.

ρ = 1025 kg/m³v = 3 m/sd = 80 mm
ṁ = kg/s
2.Easy
12d1​ = 75 mm, v1​ = 0.75 m/sd2​ = 25 mm, v2​ = ?

Water flows through a pipe that narrows from 75 mm to 25 mm in diameter. The velocity in the wide section is 0.75 m/s. Find the velocity v2 in the narrow section.

d1 = 75 mmd2 = 25 mmv1 = 0.75 m/s
v2 = m/s
3.Medium
12d1​ = 75 mm, p1​ = 300 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 300 kPa and the velocity is 2.25 m/s. Ignoring losses, find the pressure p2 in the narrow section.

d1 = 75 mmd2 = 40 mmp1 = 300 kPav1 = 2.25 m/sρ = 1000 kg/m³
p2 = kPa
4.Medium
d1​ = 150 mmd2​ = 75 mm12p1​ − p2​ = 32 kPaQ = ?

Water flows through a horizontal venturi meter with an inlet diameter of 150 mm and a throat diameter of 75 mm. The pressure at the inlet is 32 kPa higher than at the throat. Ignoring losses, find the flow rate Q.

d1 = 150 mmd2 = 75 mmp1 − p2 = 32 kPaρ = 1000 kg/m³
Q = L/s
5.Hard
pair​ = 140 kPav = ?d = 40 mmh = 1 m

A closed water tank has compressed air above the water at a gauge pressure of 140 kPa. Water leaves through an opening with a diameter of 40 mm, 1 m below the water surface, into the open air. Ignoring losses, find the jet velocity v. Use g = 9.81 m/s².

pair = 140 kPa (gauge)h = 1 md = 40 mmρ = 1000 kg/m³g = 9.81 m/s²
v = m/s
6.Hard
12d1​ = 75 mm, p1​ = 180 kPad2​ = 40 mm, p2​ = ?Δz = 7 m

Water flows up through a pipe that narrows from 75 mm to 40 mm while rising 7 m. At section 1 the pressure is 180 kPa and the velocity is 2.25 m/s. Ignoring losses, find the pressure p2 at section 2.

d1 = 75 mmd2 = 40 mmp1 = 180 kPav1 = 2.25 m/sΔz = 7 mρ = 1000 kg/m³
p2 = kPa

Answer key

  1. 1. ṁ = 15.46 kg/s
  2. 2. v2 = 6.75 m/s
  3. 3. p2 = 271.2 kPa
  4. 4. Q = 36.5 L/s
  5. 5. v = 17.31 m/s
  6. 6. p2 = 82.58 kPa

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