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 = ?

Oil (ρ = 880 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 = 880 kg/m³v = 1.5 m/sd = 100 mm
ṁ = kg/s
2.Easy
12d1​ = 150 mm, v1​ = 0.5 m/sd2​ = 50 mm

Water flows at 0.5 m/s through the wide section of the pipe, which has a diameter of 150 mm. Find the volume flow rate Q.

d1 = 150 mmd2 = 50 mmv1 = 0.5 m/s
Q = L/s
3.Medium
v = ?p0​pp0​ − p = 19 kPastagnation point

A pitot-static tube in a water pipe reads a difference of 19 kPa between the stagnation pressure and the static pressure. Find the water velocity v at the tip.

p0 − p = 19 kPaρ = 1000 kg/m³
v = m/s
4.Medium
v = ?p0​pp0​ − p = 1300 Pastagnation point

A pitot-static tube in a wind tunnel reads a difference of 1300 Pa between the stagnation pressure and the static pressure. The air density is 1.2 kg/m³. Find the air speed v.

p0 − p = 1300 Paρ = 1.2 kg/m³
v = m/s
5.Hard
12d1​ = 150 mm, p1​ = 180 kPad2​ = 100 mm, p2​ = ?Δz = 5 m

Water flows up through a pipe that narrows from 150 mm to 100 mm while rising 5 m. At section 1 the pressure is 180 kPa and the velocity is 1.75 m/s. Ignoring losses, find the pressure p2 at section 2.

d1 = 150 mmd2 = 100 mmp1 = 180 kPav1 = 1.75 m/sΔz = 5 mρ = 1000 kg/m³
p2 = kPa
6.Hard
12d1​ = 150 mm, p1​ = 350 kPad2​ = 75 mm, p2​ = ?Δz = 4 m

Water flows up through a pipe that narrows from 150 mm to 75 mm while rising 4 m. At section 1 the pressure is 350 kPa and the velocity is 2.25 m/s. Ignoring losses, find the pressure p2 at section 2.

d1 = 150 mmd2 = 75 mmp1 = 350 kPav1 = 2.25 m/sΔz = 4 mρ = 1000 kg/m³
p2 = kPa

Answer key

  1. 1. ṁ = 10.37 kg/s
  2. 2. Q = 8.836 L/s
  3. 3. v = 6.164 m/s
  4. 4. v = 46.55 m/s
  5. 5. p2 = 124.7 kPa
  6. 6. p2 = 272.8 kPa

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