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​ = 75 mm, v2​ = ?

Water flows through a pipe that narrows from 150 mm to 75 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 = 75 mmv1 = 1.25 m/s
v2 = m/s
2.Easy
12Q = 34 L/sv = 1.5 m/s, d = ?

A water line must carry 34 L/s. To limit noise and wear, the mean velocity should be 1.5 m/s. Find the inner pipe diameter d needed.

Q = 34 L/sv = 1.5 m/s
d = mm
3.Medium
12d1​ = 200 mm, p1​ = 360 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 360 kPa and the velocity is 1 m/s. Ignoring losses, find the pressure p2 in the narrow section.

d1 = 200 mmd2 = 75 mmp1 = 360 kPav1 = 1 m/sρ = 1000 kg/m³
p2 = kPa
4.Medium
12d1​ = 75 mm, p1​ = 370 kPad2​ = 50 mm, p2​ = ?

Water flows through a horizontal pipe that narrows from 75 mm to 50 mm. In the wide section the pressure is 370 kPa and the velocity is 1.5 m/s. Ignoring losses, find the pressure p2 in the narrow section.

d1 = 75 mmd2 = 50 mmp1 = 370 kPav1 = 1.5 m/sρ = 1000 kg/m³
p2 = kPa
5.Hard
12d1​ = 75 mm, p1​ = 310 kPad2​ = 40 mm, p2​ = ?Δz = 8 m

Water flows up through a pipe that narrows from 75 mm to 40 mm while rising 8 m. At section 1 the pressure is 310 kPa and the velocity is 1.5 m/s. Ignoring losses, find the pressure p2 at section 2.

d1 = 75 mmd2 = 40 mmp1 = 310 kPav1 = 1.5 m/sΔz = 8 mρ = 1000 kg/m³
p2 = kPa
6.Hard
d1​ = 150 mmd2​ = 75 mm12Δh = 200 mmmercuryQ = ?

A horizontal venturi meter (inlet 150 mm, throat 75 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 0.96. 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 = 150 mmd2 = 75 mmΔh = 200 mmCd = 0.96ρHg = 13 600 kg/m³g = 9.81 m/s²
Q = L/s

Answer key

  1. 1. v2 = 5 m/s
  2. 2. d = 169.9 mm
  3. 3. p2 = 335.2 kPa
  4. 4. p2 = 365.4 kPa
  5. 5. p2 = 218.7 kPa
  6. 6. Q = 30.8 L/s

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