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 = 2.5 m/s, d = ?

A water line must carry 41 L/s. To limit noise and wear, the mean velocity should be 2.5 m/s. Find the inner pipe diameter d needed.

Q = 41 L/sv = 2.5 m/s
d = mm
2.Easy
12d1​ = 150 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 150 mm. Find the volume flow rate Q.

d1 = 150 mmd2 = 50 mmv1 = 1.5 m/s
Q = L/s
3.Medium
v = ?p0​pp0​ − p = 20 kPastagnation point

A pitot-static tube in a water pipe reads a difference of 20 kPa between the stagnation pressure and the static pressure. Find the water velocity v at the tip.

p0 − p = 20 kPaρ = 1000 kg/m³
v = m/s
4.Medium
12d1​ = 100 mm, p1​ = 110 kPad2​ = 75 mm, p2​ = ?

Water flows through a horizontal pipe that narrows from 100 mm to 75 mm. In the wide section the pressure is 110 kPa and the velocity is 2.5 m/s. Ignoring losses, find the pressure p2 in the narrow section.

d1 = 100 mmd2 = 75 mmp1 = 110 kPav1 = 2.5 m/sρ = 1000 kg/m³
p2 = kPa
5.Hard
12d1​ = 150 mm, p1​ = 140 kPad2​ = 40 mm, p2​ = ?Δz = 4 m

Water flows up through a pipe that narrows from 150 mm to 40 mm while rising 4 m. At section 1 the pressure is 140 kPa and the velocity is 0.5 m/s. Ignoring losses, find the pressure p2 at section 2.

d1 = 150 mmd2 = 40 mmp1 = 140 kPav1 = 0.5 m/sΔz = 4 mρ = 1000 kg/m³
p2 = kPa
6.Hard
C211.5 m2.5 md = 20 mmpC​ = ?

A hose with an inner diameter of 20 mm siphons water from an open tank. The highest point C of the hose is 1.5 m above the water surface, and the outlet (open to the air) is 2.5 m below the water surface. Ignore losses and take g = 9.81 m/s². Find the absolute pressure pC at point C. The atmospheric pressure is 101.3 kPa.

d = 20 mmzC = +1.5 mz2 = −2.5 mg = 9.81 m/s²patm = 101.3 kPa
pC = kPa

Answer key

  1. 1. d = 144.5 mm
  2. 2. Q = 26.51 L/s
  3. 3. v = 6.325 m/s
  4. 4. p2 = 103.2 kPa
  5. 5. p2 = 76.17 kPa
  6. 6. pC = 62.06 kPa

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