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 = 2.5 m/sṁ = ?

Oil (ρ = 880 kg/m³) flows at 2.5 m/s through a pipe with an inner diameter of 100 mm. Find the mass flow rate ṁ.

ρ = 880 kg/m³v = 2.5 m/sd = 100 mm
ṁ = kg/s
2.Easy
12Q = 38 L/sv = 2 m/s, d = ?

A water line must carry 38 L/s. To limit noise and wear, the mean velocity should be 2 m/s. Find the inner pipe diameter d needed.

Q = 38 L/sv = 2 m/s
d = mm
3.Medium
12d1​ = 150 mm, p1​ = 170 kPad2​ = 75 mm, p2​ = ?

Water flows through a horizontal pipe that narrows from 150 mm to 75 mm. In the wide section the pressure is 170 kPa and the velocity is 2 m/s. Ignoring losses, find the pressure p2 in the narrow section.

d1 = 150 mmd2 = 75 mmp1 = 170 kPav1 = 2 m/sρ = 1000 kg/m³
p2 = kPa
4.Medium
12d1​ = 75 mm, p1​ = 250 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 250 kPa and the velocity is 0.75 m/s. Ignoring losses, find the pressure p2 in the narrow section.

d1 = 75 mmd2 = 50 mmp1 = 250 kPav1 = 0.75 m/sρ = 1000 kg/m³
p2 = kPa
5.Hard
d1​ = 300 mmd2​ = 150 mm12Δh = 180 mmmercuryQ = ?

A horizontal venturi meter (inlet 300 mm, throat 150 mm) carries water. A mercury U-tube manometer connected between the inlet and the throat shows a level difference of 180 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 = 300 mmd2 = 150 mmΔh = 180 mmCd = 0.96ρHg = 13 600 kg/m³g = 9.81 m/s²
Q = L/s
6.Hard
12d1​ = 150 mm, p1​ = 180 kPad2​ = 100 mm, p2​ = ?Δz = 3 m

Water flows up through a pipe that narrows from 150 mm to 100 mm while rising 3 m. At section 1 the pressure is 180 kPa and the velocity is 0.5 m/s. Ignoring losses, find the pressure p2 at section 2.

d1 = 150 mmd2 = 100 mmp1 = 180 kPav1 = 0.5 m/sΔz = 3 mρ = 1000 kg/m³
p2 = kPa

Answer key

  1. 1. ṁ = 17.28 kg/s
  2. 2. d = 155.5 mm
  3. 3. p2 = 140 kPa
  4. 4. p2 = 248.9 kPa
  5. 5. Q = 116.9 L/s
  6. 6. p2 = 150.1 kPa

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