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 = 50 mm, v = 0.5 m/sṁ = ?

Water (ρ = 1000 kg/m³) flows at 0.5 m/s through a pipe with an inner diameter of 50 mm. Find the mass flow rate ṁ.

ρ = 1000 kg/m³v = 0.5 m/sd = 50 mm
ṁ = kg/s
2.Easy
12d = 200 mm, v = 2.75 m/sṁ = ?

Oil (ρ = 880 kg/m³) flows at 2.75 m/s through a pipe with an inner diameter of 200 mm. Find the mass flow rate ṁ.

ρ = 880 kg/m³v = 2.75 m/sd = 200 mm
ṁ = kg/s
3.Medium
v = ?p0​pp0​ − p = 350 Pastagnation point

A pitot-static tube in a wind tunnel reads a difference of 350 Pa between the stagnation pressure and the static pressure. The air density is 1.2 kg/m³. Find the air speed v.

p0 − p = 350 Paρ = 1.2 kg/m³
v = m/s
4.Medium
12d1​ = 100 mm, p1​ = 340 kPad2​ = 50 mm, p2​ = ?

Water flows through a horizontal pipe that narrows from 100 mm to 50 mm. In the wide section the pressure is 340 kPa and the velocity is 1.5 m/s. Ignoring losses, find the pressure p2 in the narrow section.

d1 = 100 mmd2 = 50 mmp1 = 340 kPav1 = 1.5 m/sρ = 1000 kg/m³
p2 = kPa
5.Hard
pair​ = 150 kPav = ?d = 40 mmh = 1 m

A closed water tank has compressed air above the water at a gauge pressure of 150 kPa. Water leaves through an opening with a diameter of 40 mm, 1 m below the water surface, into the open air. Ignoring losses, find the jet velocity v. Use g = 9.81 m/s².

pair = 150 kPa (gauge)h = 1 md = 40 mmρ = 1000 kg/m³g = 9.81 m/s²
v = m/s
6.Hard
12d1​ = 75 mm, p1​ = 290 kPad2​ = 25 mm, p2​ = ?Δz = 9 m

Water flows up through a pipe that narrows from 75 mm to 25 mm while rising 9 m. At section 1 the pressure is 290 kPa and the velocity is 0.75 m/s. Ignoring losses, find the pressure p2 at section 2.

d1 = 75 mmd2 = 25 mmp1 = 290 kPav1 = 0.75 m/sΔz = 9 mρ = 1000 kg/m³
p2 = kPa

Answer key

  1. 1. ṁ = 0.9817 kg/s
  2. 2. ṁ = 76.03 kg/s
  3. 3. v = 24.15 m/s
  4. 4. p2 = 323.1 kPa
  5. 5. v = 17.88 m/s
  6. 6. p2 = 179.2 kPa

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