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 = 80 mm, v = 3.75 m/sṁ = ?

Oil (ρ = 880 kg/m³) flows at 3.75 m/s through a pipe with an inner diameter of 80 mm. Find the mass flow rate ṁ.

ρ = 880 kg/m³v = 3.75 m/sd = 80 mm
ṁ = kg/s
2.Easy
12d1​ = 200 mm, v1​ = 0.5 m/sd2​ = 100 mm

Water flows at 0.5 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 = 0.5 m/s
Q = L/s
3.Medium
v = ?p0​pp0​ − p = 21 kPastagnation point

A pitot-static tube in a water pipe reads a difference of 21 kPa between the stagnation pressure and the static pressure. Find the water velocity v at the tip.

p0 − p = 21 kPaρ = 1000 kg/m³
v = m/s
4.Medium
v = ?p0​pp0​ − p = 22 kPastagnation point

A pitot-static tube in a water pipe reads a difference of 22 kPa between the stagnation pressure and the static pressure. Find the water velocity v at the tip.

p0 − p = 22 kPaρ = 1000 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 2.5 m/s. Ignoring losses, find the pressure p2 at section 2.

d1 = 150 mmd2 = 100 mmp1 = 180 kPav1 = 2.5 m/sΔz = 5 mρ = 1000 kg/m³
p2 = kPa
6.Hard
pair​ = 20 kPaQ = ?d = 25 mmh = 2.5 m

A closed water tank has compressed air above the water at a gauge pressure of 20 kPa. Water leaves through an opening with a diameter of 25 mm, 2.5 m below the water surface, into the open air. Ignoring losses, find the flow rate Q. Use g = 9.81 m/s².

pair = 20 kPa (gauge)h = 2.5 md = 25 mmρ = 1000 kg/m³g = 9.81 m/s²
Q = L/s

Answer key

  1. 1. ṁ = 16.59 kg/s
  2. 2. Q = 15.71 L/s
  3. 3. v = 6.481 m/s
  4. 4. v = 6.633 m/s
  5. 5. p2 = 118.3 kPa
  6. 6. Q = 4.632 L/s

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