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 = 24 L/sv = 1 m/s, d = ?

A water line must carry 24 L/s. To limit noise and wear, the mean velocity should be 1 m/s. Find the inner pipe diameter d needed.

Q = 24 L/sv = 1 m/s
d = mm
2.Easy
12d1​ = 100 mm, v1​ = 2 m/sd2​ = 50 mm

Water flows at 2 m/s through the wide section of the pipe, which has a diameter of 100 mm. Find the volume flow rate Q.

d1 = 100 mmd2 = 50 mmv1 = 2 m/s
Q = L/s
3.Medium
12d1​ = 75 mm, p1​ = 310 kPad2​ = 50 mm, p2​ = ?

Water flows through a horizontal pipe that narrows from 75 mm to 50 mm. In the wide section the pressure is 310 kPa and the velocity is 2 m/s. Ignoring losses, find the pressure p2 in the narrow section.

d1 = 75 mmd2 = 50 mmp1 = 310 kPav1 = 2 m/sρ = 1000 kg/m³
p2 = kPa
4.Medium
12d1​ = 80 mm, p1​ = ?d2​ = 40 mm, p2​ = 250 kPa

Water flows at 14 L/s through a horizontal pipe that narrows from 80 mm to 40 mm. The pressure in the narrow section is 250 kPa. Ignoring losses, find the pressure p1 in the wide section.

Q = 14 L/sd1 = 80 mmd2 = 40 mmp2 = 250 kPaρ = 1000 kg/m³
p1 = kPa
5.Hard
12d1​ = 100 mm, p1​ = 120 kPad2​ = 75 mm, p2​ = ?Δz = 1 m

Water flows up through a pipe that narrows from 100 mm to 75 mm while rising 1 m. At section 1 the pressure is 120 kPa and the velocity is 1.75 m/s. Ignoring losses, find the pressure p2 at section 2.

d1 = 100 mmd2 = 75 mmp1 = 120 kPav1 = 1.75 m/sΔz = 1 mρ = 1000 kg/m³
p2 = kPa
6.Hard
C213 m3.5 md = 20 mmQ = ?

A hose with an inner diameter of 20 mm siphons water from an open tank. The highest point C of the hose is 3 m above the water surface, and the outlet (open to the air) is 3.5 m below the water surface. Ignore losses and take g = 9.81 m/s². Find the flow rate Q.

d = 20 mmzC = +3 mz2 = −3.5 mg = 9.81 m/s²
Q = L/s

Answer key

  1. 1. d = 174.8 mm
  2. 2. Q = 15.71 L/s
  3. 3. p2 = 301.9 kPa
  4. 4. p1 = 308.2 kPa
  5. 5. p2 = 106.9 kPa
  6. 6. Q = 2.603 L/s

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