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 = 1.75 m/sṁ = ?

Oil (ρ = 880 kg/m³) flows at 1.75 m/s through a pipe with an inner diameter of 80 mm. Find the mass flow rate ṁ.

ρ = 880 kg/m³v = 1.75 m/sd = 80 mm
ṁ = kg/s
2.Easy
12d1​ = 100 mm, v1​ = 1 m/sd2​ = 40 mm

Water flows at 1 m/s through the wide section of the pipe, which has a diameter of 100 mm. Find the volume flow rate Q.

d1 = 100 mmd2 = 40 mmv1 = 1 m/s
Q = L/s
3.Medium
12d1​ = 75 mm, p1​ = 100 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 100 kPa and the velocity is 3 m/s. Ignoring losses, find the pressure p2 in the narrow section.

d1 = 75 mmd2 = 50 mmp1 = 100 kPav1 = 3 m/sρ = 1000 kg/m³
p2 = kPa
4.Medium
12d1​ = 150 mm, p1​ = ?d2​ = 75 mm, p2​ = 110 kPa

Water flows at 5 L/s through a horizontal pipe that narrows from 150 mm to 75 mm. The pressure in the narrow section is 110 kPa. Ignoring losses, find the pressure p1 in the wide section.

Q = 5 L/sd1 = 150 mmd2 = 75 mmp2 = 110 kPaρ = 1000 kg/m³
p1 = kPa
5.Hard
12d1​ = 100 mm, p1​ = 210 kPad2​ = 50 mm, p2​ = ?Δz = 5 m

Water flows up through a pipe that narrows from 100 mm to 50 mm while rising 5 m. At section 1 the pressure is 210 kPa and the velocity is 1.5 m/s. Ignoring losses, find the pressure p2 at section 2.

d1 = 100 mmd2 = 50 mmp1 = 210 kPav1 = 1.5 m/sΔz = 5 mρ = 1000 kg/m³
p2 = kPa
6.Hard
pair​ = 30 kPav = ?d = 50 mmh = 3 m

A closed water tank has compressed air above the water at a gauge pressure of 30 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 jet velocity v. Use g = 9.81 m/s².

pair = 30 kPa (gauge)h = 3 md = 50 mmρ = 1000 kg/m³g = 9.81 m/s²
v = m/s

Answer key

  1. 1. ṁ = 7.741 kg/s
  2. 2. Q = 7.854 L/s
  3. 3. p2 = 81.72 kPa
  4. 4. p1 = 110.6 kPa
  5. 5. p2 = 144.1 kPa
  6. 6. v = 10.9 m/s

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