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​ = 2 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 2 m/s. Find the velocity v2 in the narrow section.

d1 = 150 mmd2 = 75 mmv1 = 2 m/s
v2 = m/s
2.Easy
v = ?h = 5 m

An open water tank drains through a small opening in its side. The free surface is 5 m above the opening. Ignoring losses, find the jet velocity v at the opening. Use g = 9.81 m/s².

h = 5 mg = 9.81 m/s²
v = m/s
3.Medium
12d1​ = 100 mm, p1​ = 280 kPad2​ = 75 mm, p2​ = ?

Water flows through a horizontal pipe that narrows from 100 mm to 75 mm. In the wide section the pressure is 280 kPa and the velocity is 2.5 m/s. Ignoring losses, find the pressure p2 in the narrow section.

d1 = 100 mmd2 = 75 mmp1 = 280 kPav1 = 2.5 m/sρ = 1000 kg/m³
p2 = kPa
4.Medium
12d1​ = 200 mm, p1​ = 230 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 230 kPa and the velocity is 1.75 m/s. Ignoring losses, find the pressure p2 in the narrow section.

d1 = 200 mmd2 = 100 mmp1 = 230 kPav1 = 1.75 m/sρ = 1000 kg/m³
p2 = kPa
5.Hard
H = ?d1​ = 50 mmp1​ = 50 kPad2​ = 20 mm

A fountain nozzle points straight up. Just below the nozzle the supply pipe has a diameter of 50 mm and a gauge pressure of 50 kPa. The nozzle exit diameter is 20 mm, and the height difference across the nozzle is negligible. Ignoring losses and air resistance, find the height H the jet rises above the nozzle. Use g = 9.81 m/s².

d1 = 50 mmp1 = 50 kPa (gauge)d2 = 20 mmρ = 1000 kg/m³g = 9.81 m/s²
H = m
6.Hard
12d1​ = 200 mm, p1​ = 330 kPad2​ = 75 mm, p2​ = ?Δz = 9 m

Water flows up through a pipe that narrows from 200 mm to 75 mm while rising 9 m. At section 1 the pressure is 330 kPa and the velocity is 1.75 m/s. Ignoring losses, find the pressure p2 at section 2.

d1 = 200 mmd2 = 75 mmp1 = 330 kPav1 = 1.75 m/sΔz = 9 mρ = 1000 kg/m³
p2 = kPa

Answer key

  1. 1. v2 = 8 m/s
  2. 2. v = 9.905 m/s
  3. 3. p2 = 273.2 kPa
  4. 4. p2 = 207 kPa
  5. 5. H = 5.231 m
  6. 6. p2 = 165.8 kPa

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