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 = 80 mm, v = 2.25 m/sṁ = ?

Oil (ρ = 880 kg/m³) flows at 2.25 m/s through a pipe with an inner diameter of 80 mm. Find the mass flow rate ṁ.

ρ = 880 kg/m³v = 2.25 m/sd = 80 mm
ṁ = kg/s
2.Easy
vd = 40 mmh = 7.5 m

An open water tank drains through a round opening with a diameter of 40 mm in its side. The free surface is 7.5 m above the opening. Ignoring losses and the contraction of the jet, find the flow rate Q. Use g = 9.81 m/s².

h = 7.5 mg = 9.81 m/s²d = 40 mm
Q = L/s
3.Medium
12d1​ = 150 mm, p1​ = 380 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 380 kPa and the velocity is 3 m/s. Ignoring losses, find the pressure p2 in the narrow section.

d1 = 150 mmd2 = 75 mmp1 = 380 kPav1 = 3 m/sρ = 1000 kg/m³
p2 = kPa
4.Medium
12d1​ = 200 mm, p1​ = 130 kPad2​ = 100 mm, p2​ = ?

Water flows through a horizontal pipe that narrows from 200 mm to 100 mm. In the wide section the pressure is 130 kPa and the velocity is 1.5 m/s. Ignoring losses, find the pressure p2 in the narrow section.

d1 = 200 mmd2 = 100 mmp1 = 130 kPav1 = 1.5 m/sρ = 1000 kg/m³
p2 = kPa
5.Hard
12d1​ = 75 mm, p1​ = 390 kPad2​ = 50 mm, p2​ = ?Δz = 2 m

Water flows up through a pipe that narrows from 75 mm to 50 mm while rising 2 m. At section 1 the pressure is 390 kPa and the velocity is 1.5 m/s. Ignoring losses, find the pressure p2 at section 2.

d1 = 75 mmd2 = 50 mmp1 = 390 kPav1 = 1.5 m/sΔz = 2 mρ = 1000 kg/m³
p2 = kPa
6.Hard
12d1​ = 150 mm, p1​ = 260 kPad2​ = 75 mm, p2​ = ?Δz = 4 m

Water flows up through a pipe that narrows from 150 mm to 75 mm while rising 4 m. At section 1 the pressure is 260 kPa and the velocity is 0.5 m/s. Ignoring losses, find the pressure p2 at section 2.

d1 = 150 mmd2 = 75 mmp1 = 260 kPav1 = 0.5 m/sΔz = 4 mρ = 1000 kg/m³
p2 = kPa

Answer key

  1. 1. ṁ = 9.953 kg/s
  2. 2. Q = 15.24 L/s
  3. 3. p2 = 312.5 kPa
  4. 4. p2 = 113.1 kPa
  5. 5. p2 = 365.8 kPa
  6. 6. p2 = 218.9 kPa

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