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
12d1​ = 200 mm, v1​ = 2.25 m/sd2​ = 100 mm

Water flows at 2.25 m/s through the wide section of the pipe, which has a diameter of 200 mm. Find the volume flow rate Q.

d1 = 200 mmd2 = 100 mmv1 = 2.25 m/s
Q = L/s
2.Easy
12d = 50 mm, v = 0.75 m/sṁ = ?

Glycerin (ρ = 1260 kg/m³) flows at 0.75 m/s through a pipe with an inner diameter of 50 mm. Find the mass flow rate ṁ.

ρ = 1260 kg/m³v = 0.75 m/sd = 50 mm
ṁ = kg/s
3.Medium
12d1​ = 75 mm, p1​ = 300 kPad2​ = 40 mm, p2​ = ?

Water flows through a horizontal pipe that narrows from 75 mm to 40 mm. In the wide section the pressure is 300 kPa and the velocity is 2.75 m/s. Ignoring losses, find the pressure p2 in the narrow section.

d1 = 75 mmd2 = 40 mmp1 = 300 kPav1 = 2.75 m/sρ = 1000 kg/m³
p2 = kPa
4.Medium
v = ?p0​pp0​ − p = 400 Pastagnation point

A pitot-static tube in a wind tunnel reads a difference of 400 Pa between the stagnation pressure and the static pressure. The air density is 1.2 kg/m³. Find the air speed v.

p0 − p = 400 Paρ = 1.2 kg/m³
v = m/s
5.Hard
pair​ = 60 kPav = ?d = 40 mmh = 1.5 m

A closed water tank has compressed air above the water at a gauge pressure of 60 kPa. Water leaves through an opening with a diameter of 40 mm, 1.5 m below the water surface, into the open air. Ignoring losses, find the jet velocity v. Use g = 9.81 m/s².

pair = 60 kPa (gauge)h = 1.5 md = 40 mmρ = 1000 kg/m³g = 9.81 m/s²
v = m/s
6.Hard
12d1​ = 150 mm, p1​ = 250 kPad2​ = 100 mm, p2​ = ?Δz = 2 m

Water flows up through a pipe that narrows from 150 mm to 100 mm while rising 2 m. At section 1 the pressure is 250 kPa and the velocity is 1.75 m/s. Ignoring losses, find the pressure p2 at section 2.

d1 = 150 mmd2 = 100 mmp1 = 250 kPav1 = 1.75 m/sΔz = 2 mρ = 1000 kg/m³
p2 = kPa

Answer key

  1. 1. Q = 70.69 L/s
  2. 2. ṁ = 1.856 kg/s
  3. 3. p2 = 257 kPa
  4. 4. v = 25.82 m/s
  5. 5. v = 12.22 m/s
  6. 6. p2 = 224.2 kPa

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