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 = 2.25 m/sṁ = ?

Glycerin (ρ = 1260 kg/m³) flows at 2.25 m/s through a pipe with an inner diameter of 25 mm. Find the mass flow rate ṁ.

ρ = 1260 kg/m³v = 2.25 m/sd = 25 mm
ṁ = kg/s
2.Easy
12d1​ = 100 mm, v1​ = 1 m/sd2​ = 40 mm, v2​ = ?

Water flows through a pipe that narrows from 100 mm to 40 mm in diameter. The velocity in the wide section is 1 m/s. Find the velocity v2 in the narrow section.

d1 = 100 mmd2 = 40 mmv1 = 1 m/s
v2 = m/s
3.Medium
v = ?p0​pp0​ − p = 850 Pastagnation point

A pitot-static tube in a wind tunnel reads a difference of 850 Pa between the stagnation pressure and the static pressure. The air density is 1.2 kg/m³. Find the air speed v.

p0 − p = 850 Paρ = 1.2 kg/m³
v = m/s
4.Medium
v = ?p0​pp0​ − p = 10 kPastagnation point

A pitot-static tube in a water pipe reads a difference of 10 kPa between the stagnation pressure and the static pressure. Find the water velocity v at the tip.

p0 − p = 10 kPaρ = 1000 kg/m³
v = m/s
5.Hard
12d1​ = 75 mm, p1​ = 220 kPad2​ = 50 mm, p2​ = ?Δz = 8 m

Water flows up through a pipe that narrows from 75 mm to 50 mm while rising 8 m. At section 1 the pressure is 220 kPa and the velocity is 2.75 m/s. Ignoring losses, find the pressure p2 at section 2.

d1 = 75 mmd2 = 50 mmp1 = 220 kPav1 = 2.75 m/sΔz = 8 mρ = 1000 kg/m³
p2 = kPa
6.Hard
12d1​ = 150 mm, p1​ = 260 kPad2​ = 40 mm, p2​ = ?Δz = 5 m

Water flows up through a pipe that narrows from 150 mm to 40 mm while rising 5 m. At section 1 the pressure is 260 kPa and the velocity is 1 m/s. Ignoring losses, find the pressure p2 at section 2.

d1 = 150 mmd2 = 40 mmp1 = 260 kPav1 = 1 m/sΔz = 5 mρ = 1000 kg/m³
p2 = kPa

Answer key

  1. 1. ṁ = 1.392 kg/s
  2. 2. v2 = 6.25 m/s
  3. 3. v = 37.64 m/s
  4. 4. v = 4.472 m/s
  5. 5. p2 = 126.2 kPa
  6. 6. p2 = 112.6 kPa

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