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​ = 150 mm, v1​ = 1.25 m/sd2​ = 50 mm

Water flows at 1.25 m/s through the wide section of the pipe, which has a diameter of 150 mm. Find the volume flow rate Q.

d1 = 150 mmd2 = 50 mmv1 = 1.25 m/s
Q = L/s
2.Easy
12d = 25 mm, v = 2 m/sṁ = ?

Oil (ρ = 880 kg/m³) flows at 2 m/s through a pipe with an inner diameter of 25 mm. Find the mass flow rate ṁ.

ρ = 880 kg/m³v = 2 m/sd = 25 mm
ṁ = kg/s
3.Medium
12d1​ = 100 mm, p1​ = 280 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 280 kPa and the velocity is 0.75 m/s. Ignoring losses, find the pressure p2 in the narrow section.

d1 = 100 mmd2 = 75 mmp1 = 280 kPav1 = 0.75 m/sρ = 1000 kg/m³
p2 = kPa
4.Medium
12d1​ = 75 mm, p1​ = 150 kPad2​ = 25 mm, p2​ = ?

Water flows through a horizontal pipe that narrows from 75 mm to 25 mm. In the wide section the pressure is 150 kPa and the velocity is 0.5 m/s. Ignoring losses, find the pressure p2 in the narrow section.

d1 = 75 mmd2 = 25 mmp1 = 150 kPav1 = 0.5 m/sρ = 1000 kg/m³
p2 = kPa
5.Hard
12d1​ = 75 mm, p1​ = 310 kPad2​ = 25 mm, p2​ = ?Δz = 8 m

Water flows up through a pipe that narrows from 75 mm to 25 mm while rising 8 m. At section 1 the pressure is 310 kPa and the velocity is 1.25 m/s. Ignoring losses, find the pressure p2 at section 2.

d1 = 75 mmd2 = 25 mmp1 = 310 kPav1 = 1.25 m/sΔz = 8 mρ = 1000 kg/m³
p2 = kPa
6.Hard
pair​ = 170 kPaQ = ?d = 50 mmh = 3 m

A closed water tank has compressed air above the water at a gauge pressure of 170 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 = 170 kPa (gauge)h = 3 md = 50 mmρ = 1000 kg/m³g = 9.81 m/s²
Q = L/s

Answer key

  1. 1. Q = 22.09 L/s
  2. 2. ṁ = 0.8639 kg/s
  3. 3. p2 = 279.4 kPa
  4. 4. p2 = 140 kPa
  5. 5. p2 = 169 kPa
  6. 6. Q = 39.21 L/s

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