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 = 100 mm, v = 2.25 m/sṁ = ?

Seawater (ρ = 1025 kg/m³) flows at 2.25 m/s through a pipe with an inner diameter of 100 mm. Find the mass flow rate ṁ.

ρ = 1025 kg/m³v = 2.25 m/sd = 100 mm
ṁ = kg/s
2.Easy
12Q = 24 L/sv = 3 m/s, d = ?

A water line must carry 24 L/s. To limit noise and wear, the mean velocity should be 3 m/s. Find the inner pipe diameter d needed.

Q = 24 L/sv = 3 m/s
d = mm
3.Medium
Q = ?d = 20 mm, Cd​ = 0.65h = 5.5 m

Water drains from a large open tank through a sharp-edged orifice with a diameter of 20 mm. The water level is kept 5.5 m above the orifice and the discharge coefficient is 0.65. Find the flow rate Q. Use g = 9.81 m/s².

d = 20 mmh = 5.5 mCd = 0.65g = 9.81 m/s²
Q = L/s
4.Medium
12d1​ = 200 mm, p1​ = 320 kPad2​ = 40 mm, p2​ = ?

Water flows through a horizontal pipe that narrows from 200 mm to 40 mm. In the wide section the pressure is 320 kPa and the velocity is 0.5 m/s. Ignoring losses, find the pressure p2 in the narrow section.

d1 = 200 mmd2 = 40 mmp1 = 320 kPav1 = 0.5 m/sρ = 1000 kg/m³
p2 = kPa
5.Hard
12d1​ = 150 mm, p1​ = 250 kPad2​ = 75 mm, p2​ = ?Δz = 5 m

Water flows up through a pipe that narrows from 150 mm to 75 mm while rising 5 m. At section 1 the pressure is 250 kPa and the velocity is 2 m/s. Ignoring losses, find the pressure p2 at section 2.

d1 = 150 mmd2 = 75 mmp1 = 250 kPav1 = 2 m/sΔz = 5 mρ = 1000 kg/m³
p2 = kPa
6.Hard
12d1​ = 200 mm, p1​ = 360 kPad2​ = 100 mm, p2​ = ?Δz = 6 m

Water flows up through a pipe that narrows from 200 mm to 100 mm while rising 6 m. At section 1 the pressure is 360 kPa and the velocity is 1.5 m/s. Ignoring losses, find the pressure p2 at section 2.

d1 = 200 mmd2 = 100 mmp1 = 360 kPav1 = 1.5 m/sΔz = 6 mρ = 1000 kg/m³
p2 = kPa

Answer key

  1. 1. ṁ = 18.11 kg/s
  2. 2. d = 100.9 mm
  3. 3. Q = 2.121 L/s
  4. 4. p2 = 242 kPa
  5. 5. p2 = 170.9 kPa
  6. 6. p2 = 284.3 kPa

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