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​ = 0.5 m/sd2​ = 100 mm

Water flows at 0.5 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 = 100 mmv1 = 0.5 m/s
Q = L/s
2.Easy
12d = 100 mm, v = 4 m/sṁ = ?

Seawater (ρ = 1025 kg/m³) flows at 4 m/s through a pipe with an inner diameter of 100 mm. Find the mass flow rate ṁ.

ρ = 1025 kg/m³v = 4 m/sd = 100 mm
ṁ = kg/s
3.Medium
Q = ?d = 50 mm, Cd​ = 0.61h = 6 m

Water drains from a large open tank through a sharp-edged orifice with a diameter of 50 mm. The water level is kept 6 m above the orifice and the discharge coefficient is 0.61. Find the flow rate Q. Use g = 9.81 m/s².

d = 50 mmh = 6 mCd = 0.61g = 9.81 m/s²
Q = L/s
4.Medium
12d1​ = 100 mm, p1​ = ?d2​ = 75 mm, p2​ = 70 kPa

Water flows at 10 L/s through a horizontal pipe that narrows from 100 mm to 75 mm. The pressure in the narrow section is 70 kPa. Ignoring losses, find the pressure p1 in the wide section.

Q = 10 L/sd1 = 100 mmd2 = 75 mmp2 = 70 kPaρ = 1000 kg/m³
p1 = kPa
5.Hard
12d1​ = 200 mm, p1​ = 390 kPad2​ = 100 mm, p2​ = ?Δz = 3 m

Water flows up through a pipe that narrows from 200 mm to 100 mm while rising 3 m. At section 1 the pressure is 390 kPa and the velocity is 2 m/s. Ignoring losses, find the pressure p2 at section 2.

d1 = 200 mmd2 = 100 mmp1 = 390 kPav1 = 2 m/sΔz = 3 mρ = 1000 kg/m³
p2 = kPa
6.Hard
12d1​ = 75 mm, p1​ = 170 kPad2​ = 40 mm, p2​ = ?Δz = 3 m

Water flows up through a pipe that narrows from 75 mm to 40 mm while rising 3 m. At section 1 the pressure is 170 kPa and the velocity is 1.25 m/s. Ignoring losses, find the pressure p2 at section 2.

d1 = 75 mmd2 = 40 mmp1 = 170 kPav1 = 1.25 m/sΔz = 3 mρ = 1000 kg/m³
p2 = kPa

Answer key

  1. 1. Q = 8.836 L/s
  2. 2. ṁ = 32.2 kg/s
  3. 3. Q = 13 L/s
  4. 4. p1 = 71.75 kPa
  5. 5. p2 = 330.6 kPa
  6. 6. p2 = 131.7 kPa

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