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​ = 75 mm, v1​ = 1.5 m/sd2​ = 40 mm

Water flows at 1.5 m/s through the wide section of the pipe, which has a diameter of 75 mm. Find the volume flow rate Q.

d1 = 75 mmd2 = 40 mmv1 = 1.5 m/s
Q = L/s
2.Easy
12d1​ = 150 mm, v1​ = 1.25 m/sd2​ = 50 mm, v2​ = ?

Water flows through a pipe that narrows from 150 mm to 50 mm in diameter. The velocity in the wide section is 1.25 m/s. Find the velocity v2 in the narrow section.

d1 = 150 mmd2 = 50 mmv1 = 1.25 m/s
v2 = m/s
3.Medium
12d1​ = 200 mm, p1​ = 180 kPad2​ = 75 mm, p2​ = ?

Water flows through a horizontal pipe that narrows from 200 mm to 75 mm. In the wide section the pressure is 180 kPa and the velocity is 1 m/s. Ignoring losses, find the pressure p2 in the narrow section.

d1 = 200 mmd2 = 75 mmp1 = 180 kPav1 = 1 m/sρ = 1000 kg/m³
p2 = kPa
4.Medium
12d1​ = 100 mm, p1​ = 280 kPad2​ = 50 mm, p2​ = ?

Water flows through a horizontal pipe that narrows from 100 mm to 50 mm. In the wide section the pressure is 280 kPa and the velocity is 1.5 m/s. Ignoring losses, find the pressure p2 in the narrow section.

d1 = 100 mmd2 = 50 mmp1 = 280 kPav1 = 1.5 m/sρ = 1000 kg/m³
p2 = kPa
5.Hard
d1​ = 250 mmd2​ = 125 mm12Δh = 230 mmmercuryQ = ?

A horizontal venturi meter (inlet 250 mm, throat 125 mm) carries water. A mercury U-tube manometer connected between the inlet and the throat shows a level difference of 230 mm. The discharge coefficient is 0.99. 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 = 250 mmd2 = 125 mmΔh = 230 mmCd = 0.99ρHg = 13 600 kg/m³g = 9.81 m/s²
Q = L/s
6.Hard
12d1​ = 200 mm, p1​ = 280 kPad2​ = 50 mm, p2​ = ?Δz = 2 m

Water flows up through a pipe that narrows from 200 mm to 50 mm while rising 2 m. At section 1 the pressure is 280 kPa and the velocity is 0.75 m/s. Ignoring losses, find the pressure p2 at section 2.

d1 = 200 mmd2 = 50 mmp1 = 280 kPav1 = 0.75 m/sΔz = 2 mρ = 1000 kg/m³
p2 = kPa

Answer key

  1. 1. Q = 6.627 L/s
  2. 2. v2 = 11.25 m/s
  3. 3. p2 = 155.2 kPa
  4. 4. p2 = 263.1 kPa
  5. 5. Q = 94.61 L/s
  6. 6. p2 = 188.7 kPa

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