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
12Q = 41 L/sv = 1.5 m/s, d = ?

A water line must carry 41 L/s. To limit noise and wear, the mean velocity should be 1.5 m/s. Find the inner pipe diameter d needed.

Q = 41 L/sv = 1.5 m/s
d = mm
2.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
3.Medium
12d1​ = 100 mm, p1​ = ?d2​ = 75 mm, p2​ = 60 kPa

Water flows at 29 L/s through a horizontal pipe that narrows from 100 mm to 75 mm. The pressure in the narrow section is 60 kPa. Ignoring losses, find the pressure p1 in the wide section.

Q = 29 L/sd1 = 100 mmd2 = 75 mmp2 = 60 kPaρ = 1000 kg/m³
p1 = kPa
4.Medium
v = ?p0​pp0​ − p = 18 kPastagnation point

A pitot-static tube in a water pipe reads a difference of 18 kPa between the stagnation pressure and the static pressure. Find the water velocity v at the tip.

p0 − p = 18 kPaρ = 1000 kg/m³
v = m/s
5.Hard
pair​ = 150 kPav = ?d = 40 mmh = 3 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, 3 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 = 3 md = 40 mmρ = 1000 kg/m³g = 9.81 m/s²
v = m/s
6.Hard
12d1​ = 200 mm, p1​ = 270 kPad2​ = 100 mm, p2​ = ?Δz = 5 m

Water flows up through a pipe that narrows from 200 mm to 100 mm while rising 5 m. At section 1 the pressure is 270 kPa and the velocity is 3 m/s. Ignoring losses, find the pressure p2 at section 2.

d1 = 200 mmd2 = 100 mmp1 = 270 kPav1 = 3 m/sΔz = 5 mρ = 1000 kg/m³
p2 = kPa

Answer key

  1. 1. d = 186.6 mm
  2. 2. ṁ = 27.17 kg/s
  3. 3. p1 = 74.73 kPa
  4. 4. v = 6 m/s
  5. 5. v = 18.94 m/s
  6. 6. p2 = 153.4 kPa

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