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 = 150 mm, v = 1.5 m/sṁ = ?

Seawater (ρ = 1025 kg/m³) flows at 1.5 m/s through a pipe with an inner diameter of 150 mm. Find the mass flow rate ṁ.

ρ = 1025 kg/m³v = 1.5 m/sd = 150 mm
ṁ = kg/s
2.Easy
12d1​ = 75 mm, v1​ = 1.5 m/sd2​ = 50 mm

Water flows at 1.5 m/s through the wide section of the pipe, which has a diameter of 75 mm. Find the volume flow rate Q.

d1 = 75 mmd2 = 50 mmv1 = 1.5 m/s
Q = L/s
3.Medium
Q = ?d = 40 mm, Cd​ = 0.63h = 4.5 m

Water drains from a large open tank through a sharp-edged orifice with a diameter of 40 mm. The water level is kept 4.5 m above the orifice and the discharge coefficient is 0.63. Find the flow rate Q. Use g = 9.81 m/s².

d = 40 mmh = 4.5 mCd = 0.63g = 9.81 m/s²
Q = L/s
4.Medium
v = ?p0​pp0​ − p = 650 Pastagnation point

A pitot-static tube in a wind tunnel reads a difference of 650 Pa between the stagnation pressure and the static pressure. The air density is 1.2 kg/m³. Find the air speed v.

p0 − p = 650 Paρ = 1.2 kg/m³
v = m/s
5.Hard
12d1​ = 100 mm, p1​ = 140 kPad2​ = 75 mm, p2​ = ?Δz = 6 m

Water flows up through a pipe that narrows from 100 mm to 75 mm while rising 6 m. At section 1 the pressure is 140 kPa and the velocity is 0.75 m/s. Ignoring losses, find the pressure p2 at section 2.

d1 = 100 mmd2 = 75 mmp1 = 140 kPav1 = 0.75 m/sΔz = 6 mρ = 1000 kg/m³
p2 = kPa
6.Hard
12d1​ = 75 mm, p1​ = 390 kPad2​ = 40 mm, p2​ = ?Δz = 1 m

Water flows up through a pipe that narrows from 75 mm to 40 mm while rising 1 m. At section 1 the pressure is 390 kPa and the velocity is 2.5 m/s. Ignoring losses, find the pressure p2 at section 2.

d1 = 75 mmd2 = 40 mmp1 = 390 kPav1 = 2.5 m/sΔz = 1 mρ = 1000 kg/m³
p2 = kPa

Answer key

  1. 1. ṁ = 27.17 kg/s
  2. 2. Q = 6.627 L/s
  3. 3. Q = 7.439 L/s
  4. 4. v = 32.91 m/s
  5. 5. p2 = 80.53 kPa
  6. 6. p2 = 344.7 kPa

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