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 = 25 mm, v = 0.5 m/sṁ = ?

Seawater (ρ = 1025 kg/m³) flows at 0.5 m/s through a pipe with an inner diameter of 25 mm. Find the mass flow rate ṁ.

ρ = 1025 kg/m³v = 0.5 m/sd = 25 mm
ṁ = kg/s
2.Easy
v = ?h = 8 m

An open water tank drains through a small opening in its side. The free surface is 8 m above the opening. Ignoring losses, find the jet velocity v at the opening. Use g = 9.81 m/s².

h = 8 mg = 9.81 m/s²
v = m/s
3.Medium
12d1​ = 200 mm, p1​ = 100 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 100 kPa and the velocity is 1.75 m/s. Ignoring losses, find the pressure p2 in the narrow section.

d1 = 200 mmd2 = 100 mmp1 = 100 kPav1 = 1.75 m/sρ = 1000 kg/m³
p2 = kPa
4.Medium
12d1​ = 100 mm, p1​ = ?d2​ = 50 mm, p2​ = 180 kPa

Water flows at 7 L/s through a horizontal pipe that narrows from 100 mm to 50 mm. The pressure in the narrow section is 180 kPa. Ignoring losses, find the pressure p1 in the wide section.

Q = 7 L/sd1 = 100 mmd2 = 50 mmp2 = 180 kPaρ = 1000 kg/m³
p1 = kPa
5.Hard
12d1​ = 75 mm, p1​ = 100 kPad2​ = 40 mm, p2​ = ?Δz = 6 m

Water flows up through a pipe that narrows from 75 mm to 40 mm while rising 6 m. At section 1 the pressure is 100 kPa and the velocity is 1.75 m/s. Ignoring losses, find the pressure p2 at section 2.

d1 = 75 mmd2 = 40 mmp1 = 100 kPav1 = 1.75 m/sΔz = 6 mρ = 1000 kg/m³
p2 = kPa
6.Hard
12d1​ = 200 mm, p1​ = 250 kPad2​ = 75 mm, p2​ = ?Δz = 4 m

Water flows up through a pipe that narrows from 200 mm to 75 mm while rising 4 m. At section 1 the pressure is 250 kPa and the velocity is 0.75 m/s. Ignoring losses, find the pressure p2 at section 2.

d1 = 200 mmd2 = 75 mmp1 = 250 kPav1 = 0.75 m/sΔz = 4 mρ = 1000 kg/m³
p2 = kPa

Answer key

  1. 1. ṁ = 0.2516 kg/s
  2. 2. v = 12.53 m/s
  3. 3. p2 = 77.03 kPa
  4. 4. p1 = 186 kPa
  5. 5. p2 = 23.75 kPa
  6. 6. p2 = 196.8 kPa

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