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 = 100 mm, v = 1.5 m/sṁ = ?

Glycerin (ρ = 1260 kg/m³) flows at 1.5 m/s through a pipe with an inner diameter of 100 mm. Find the mass flow rate ṁ.

ρ = 1260 kg/m³v = 1.5 m/sd = 100 mm
ṁ = kg/s
2.Easy
12d1​ = 150 mm, v1​ = 1 m/sd2​ = 100 mm, v2​ = ?

Water flows through a pipe that narrows from 150 mm to 100 mm in diameter. The velocity in the wide section is 1 m/s. Find the velocity v2 in the narrow section.

d1 = 150 mmd2 = 100 mmv1 = 1 m/s
v2 = m/s
3.Medium
12d1​ = 75 mm, p1​ = 310 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 310 kPa and the velocity is 1.5 m/s. Ignoring losses, find the pressure p2 in the narrow section.

d1 = 75 mmd2 = 50 mmp1 = 310 kPav1 = 1.5 m/sρ = 1000 kg/m³
p2 = kPa
4.Medium
12d1​ = 75 mm, p1​ = 120 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 120 kPa and the velocity is 0.75 m/s. Ignoring losses, find the pressure p2 in the narrow section.

d1 = 75 mmd2 = 50 mmp1 = 120 kPav1 = 0.75 m/sρ = 1000 kg/m³
p2 = kPa
5.Hard
H = ?d1​ = 50 mmp1​ = 150 kPad2​ = 30 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 150 kPa. The nozzle exit diameter is 30 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 = 150 kPa (gauge)d2 = 30 mmρ = 1000 kg/m³g = 9.81 m/s²
H = m
6.Hard
12d1​ = 200 mm, p1​ = 400 kPad2​ = 100 mm, p2​ = ?Δz = 2 m

Water flows up through a pipe that narrows from 200 mm to 100 mm while rising 2 m. At section 1 the pressure is 400 kPa and the velocity is 1.5 m/s. Ignoring losses, find the pressure p2 at section 2.

d1 = 200 mmd2 = 100 mmp1 = 400 kPav1 = 1.5 m/sΔz = 2 mρ = 1000 kg/m³
p2 = kPa

Answer key

  1. 1. ṁ = 14.84 kg/s
  2. 2. v2 = 2.25 m/s
  3. 3. p2 = 305.4 kPa
  4. 4. p2 = 118.9 kPa
  5. 5. H = 17.57 m
  6. 6. p2 = 363.5 kPa

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