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 = 200 mm, v = 1 m/sṁ = ?

Oil (ρ = 880 kg/m³) flows at 1 m/s through a pipe with an inner diameter of 200 mm. Find the mass flow rate ṁ.

ρ = 880 kg/m³v = 1 m/sd = 200 mm
ṁ = kg/s
2.Easy
12Q = 53 L/sv = 2 m/s, d = ?

A water line must carry 53 L/s. To limit noise and wear, the mean velocity should be 2 m/s. Find the inner pipe diameter d needed.

Q = 53 L/sv = 2 m/s
d = mm
3.Medium
12d1​ = 150 mm, p1​ = 170 kPad2​ = 100 mm, p2​ = ?

Water flows through a horizontal pipe that narrows from 150 mm to 100 mm. In the wide section the pressure is 170 kPa and the velocity is 2.25 m/s. Ignoring losses, find the pressure p2 in the narrow section.

d1 = 150 mmd2 = 100 mmp1 = 170 kPav1 = 2.25 m/sρ = 1000 kg/m³
p2 = kPa
4.Medium
12d1​ = 75 mm, p1​ = 180 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 180 kPa and the velocity is 2.5 m/s. Ignoring losses, find the pressure p2 in the narrow section.

d1 = 75 mmd2 = 50 mmp1 = 180 kPav1 = 2.5 m/sρ = 1000 kg/m³
p2 = kPa
5.Hard
H = ?d1​ = 75 mmp1​ = 110 kPad2​ = 40 mm

A fountain nozzle points straight up. Just below the nozzle the supply pipe has a diameter of 75 mm and a gauge pressure of 110 kPa. The nozzle exit diameter is 40 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 = 75 mmp1 = 110 kPa (gauge)d2 = 40 mmρ = 1000 kg/m³g = 9.81 m/s²
H = m
6.Hard
12d1​ = 100 mm, p1​ = 300 kPad2​ = 50 mm, p2​ = ?Δz = 10 m

Water flows up through a pipe that narrows from 100 mm to 50 mm while rising 10 m. At section 1 the pressure is 300 kPa and the velocity is 1 m/s. Ignoring losses, find the pressure p2 at section 2.

d1 = 100 mmd2 = 50 mmp1 = 300 kPav1 = 1 m/sΔz = 10 mρ = 1000 kg/m³
p2 = kPa

Answer key

  1. 1. ṁ = 27.65 kg/s
  2. 2. d = 183.7 mm
  3. 3. p2 = 159.7 kPa
  4. 4. p2 = 167.3 kPa
  5. 5. H = 12.2 m
  6. 6. p2 = 194.4 kPa

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