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 = 1 m/sṁ = ?

Oil (ρ = 880 kg/m³) flows at 1 m/s through a pipe with an inner diameter of 80 mm. Find the mass flow rate ṁ.

ρ = 880 kg/m³v = 1 m/sd = 80 mm
ṁ = kg/s
2.Easy
v = ?h = 4 m

An open water tank drains through a small opening in its side. The free surface is 4 m above the opening. Ignoring losses, find the jet velocity v at the opening. Use g = 9.81 m/s².

h = 4 mg = 9.81 m/s²
v = m/s
3.Medium
12d1​ = 75 mm, p1​ = 300 kPad2​ = 25 mm, p2​ = ?

Water flows through a horizontal pipe that narrows from 75 mm to 25 mm. In the wide section the pressure is 300 kPa and the velocity is 0.75 m/s. Ignoring losses, find the pressure p2 in the narrow section.

d1 = 75 mmd2 = 25 mmp1 = 300 kPav1 = 0.75 m/sρ = 1000 kg/m³
p2 = kPa
4.Medium
12d1​ = 100 mm, p1​ = 340 kPad2​ = 40 mm, p2​ = ?

Water flows through a horizontal pipe that narrows from 100 mm to 40 mm. In the wide section the pressure is 340 kPa and the velocity is 2 m/s. Ignoring losses, find the pressure p2 in the narrow section.

d1 = 100 mmd2 = 40 mmp1 = 340 kPav1 = 2 m/sρ = 1000 kg/m³
p2 = kPa
5.Hard
12d1​ = 75 mm, p1​ = 310 kPad2​ = 40 mm, p2​ = ?Δz = 3 m

Water flows up through a pipe that narrows from 75 mm to 40 mm while rising 3 m. At section 1 the pressure is 310 kPa and the velocity is 1 m/s. Ignoring losses, find the pressure p2 at section 2.

d1 = 75 mmd2 = 40 mmp1 = 310 kPav1 = 1 m/sΔz = 3 mρ = 1000 kg/m³
p2 = kPa
6.Hard
12d1​ = 100 mm, p1​ = 200 kPad2​ = 40 mm, p2​ = ?Δz = 2 m

Water flows up through a pipe that narrows from 100 mm to 40 mm while rising 2 m. At section 1 the pressure is 200 kPa and the velocity is 1.75 m/s. Ignoring losses, find the pressure p2 at section 2.

d1 = 100 mmd2 = 40 mmp1 = 200 kPav1 = 1.75 m/sΔz = 2 mρ = 1000 kg/m³
p2 = kPa

Answer key

  1. 1. ṁ = 4.423 kg/s
  2. 2. v = 8.859 m/s
  3. 3. p2 = 277.5 kPa
  4. 4. p2 = 263.9 kPa
  5. 5. p2 = 274.9 kPa
  6. 6. p2 = 122.1 kPa

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