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 = 40 mm, v = 3 m/sṁ = ?

Water (ρ = 1000 kg/m³) flows at 3 m/s through a pipe with an inner diameter of 40 mm. Find the mass flow rate ṁ.

ρ = 1000 kg/m³v = 3 m/sd = 40 mm
ṁ = kg/s
2.Easy
12d1​ = 150 mm, v1​ = 1.75 m/sd2​ = 75 mm, v2​ = ?

Water flows through a pipe that narrows from 150 mm to 75 mm in diameter. The velocity in the wide section is 1.75 m/s. Find the velocity v2 in the narrow section.

d1 = 150 mmd2 = 75 mmv1 = 1.75 m/s
v2 = m/s
3.Medium
12d1​ = 75 mm, p1​ = 360 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 360 kPa and the velocity is 1 m/s. Ignoring losses, find the pressure p2 in the narrow section.

d1 = 75 mmd2 = 50 mmp1 = 360 kPav1 = 1 m/sρ = 1000 kg/m³
p2 = kPa
4.Medium
12d1​ = 100 mm, p1​ = 350 kPad2​ = 75 mm, p2​ = ?

Water flows through a horizontal pipe that narrows from 100 mm to 75 mm. In the wide section the pressure is 350 kPa and the velocity is 1 m/s. Ignoring losses, find the pressure p2 in the narrow section.

d1 = 100 mmd2 = 75 mmp1 = 350 kPav1 = 1 m/sρ = 1000 kg/m³
p2 = kPa
5.Hard
pair​ = 130 kPaQ = ?d = 40 mmh = 2.5 m

A closed water tank has compressed air above the water at a gauge pressure of 130 kPa. Water leaves through an opening with a diameter of 40 mm, 2.5 m below the water surface, into the open air. Ignoring losses, find the flow rate Q. Use g = 9.81 m/s².

pair = 130 kPa (gauge)h = 2.5 md = 40 mmρ = 1000 kg/m³g = 9.81 m/s²
Q = L/s
6.Hard
12d1​ = 200 mm, p1​ = 100 kPad2​ = 75 mm, p2​ = ?Δz = 5 m

Water flows up through a pipe that narrows from 200 mm to 75 mm while rising 5 m. At section 1 the pressure is 100 kPa and the velocity is 1 m/s. Ignoring losses, find the pressure p2 at section 2.

d1 = 200 mmd2 = 75 mmp1 = 100 kPav1 = 1 m/sΔz = 5 mρ = 1000 kg/m³
p2 = kPa

Answer key

  1. 1. ṁ = 3.77 kg/s
  2. 2. v2 = 7 m/s
  3. 3. p2 = 358 kPa
  4. 4. p2 = 348.9 kPa
  5. 5. Q = 22.09 L/s
  6. 6. p2 = 26.17 kPa

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