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
12Q = 59 L/sv = 2.5 m/s, d = ?

A water line must carry 59 L/s. To limit noise and wear, the mean velocity should be 2.5 m/s. Find the inner pipe diameter d needed.

Q = 59 L/sv = 2.5 m/s
d = mm
2.Easy
12d = 150 mm, v = 2 m/sṁ = ?

Glycerin (ρ = 1260 kg/m³) flows at 2 m/s through a pipe with an inner diameter of 150 mm. Find the mass flow rate ṁ.

ρ = 1260 kg/m³v = 2 m/sd = 150 mm
ṁ = kg/s
3.Medium
12d1​ = 75 mm, p1​ = 280 kPad2​ = 40 mm, p2​ = ?

Water flows through a horizontal pipe that narrows from 75 mm to 40 mm. In the wide section the pressure is 280 kPa and the velocity is 2.25 m/s. Ignoring losses, find the pressure p2 in the narrow section.

d1 = 75 mmd2 = 40 mmp1 = 280 kPav1 = 2.25 m/sρ = 1000 kg/m³
p2 = kPa
4.Medium
12d1​ = 150 mm, p1​ = 370 kPad2​ = 50 mm, p2​ = ?

Water flows through a horizontal pipe that narrows from 150 mm to 50 mm. In the wide section the pressure is 370 kPa and the velocity is 0.75 m/s. Ignoring losses, find the pressure p2 in the narrow section.

d1 = 150 mmd2 = 50 mmp1 = 370 kPav1 = 0.75 m/sρ = 1000 kg/m³
p2 = kPa
5.Hard
d1​ = 100 mmd2​ = 60 mm12Δh = 200 mmmercuryQ = ?

A horizontal venturi meter (inlet 100 mm, throat 60 mm) carries water. A mercury U-tube manometer connected between the inlet and the throat shows a level difference of 200 mm. The discharge coefficient is 0.97. Find the flow rate Q. Use ρ = 1000 kg/m³ for water, 13 600 kg/m³ for mercury and g = 9.81 m/s².

d1 = 100 mmd2 = 60 mmΔh = 200 mmCd = 0.97ρHg = 13 600 kg/m³g = 9.81 m/s²
Q = L/s
6.Hard
12d1​ = 100 mm, p1​ = 270 kPad2​ = 75 mm, p2​ = ?Δz = 10 m

Water flows up through a pipe that narrows from 100 mm to 75 mm while rising 10 m. At section 1 the pressure is 270 kPa and the velocity is 1.25 m/s. Ignoring losses, find the pressure p2 at section 2.

d1 = 100 mmd2 = 75 mmp1 = 270 kPav1 = 1.25 m/sΔz = 10 mρ = 1000 kg/m³
p2 = kPa

Answer key

  1. 1. d = 173.3 mm
  2. 2. ṁ = 44.53 kg/s
  3. 3. p2 = 251.2 kPa
  4. 4. p2 = 347.5 kPa
  5. 5. Q = 20.67 L/s
  6. 6. p2 = 170.2 kPa

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