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​ = 150 mm, v1​ = 1.25 m/sd2​ = 100 mm

Water flows at 1.25 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 = 100 mmv1 = 1.25 m/s
Q = L/s
2.Easy
12d1​ = 75 mm, v1​ = 0.75 m/sd2​ = 40 mm, v2​ = ?

Water flows through a pipe that narrows from 75 mm to 40 mm in diameter. The velocity in the wide section is 0.75 m/s. Find the velocity v2 in the narrow section.

d1 = 75 mmd2 = 40 mmv1 = 0.75 m/s
v2 = m/s
3.Medium
12d1​ = 75 mm, p1​ = 200 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 200 kPa and the velocity is 2.25 m/s. Ignoring losses, find the pressure p2 in the narrow section.

d1 = 75 mmd2 = 50 mmp1 = 200 kPav1 = 2.25 m/sρ = 1000 kg/m³
p2 = kPa
4.Medium
12d1​ = 75 mm, p1​ = 290 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 290 kPa and the velocity is 2.5 m/s. Ignoring losses, find the pressure p2 in the narrow section.

d1 = 75 mmd2 = 40 mmp1 = 290 kPav1 = 2.5 m/sρ = 1000 kg/m³
p2 = kPa
5.Hard
C213 m3.5 md = 40 mmpC​ = ?

A hose with an inner diameter of 40 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 absolute pressure pC at point C. The atmospheric pressure is 101.3 kPa.

d = 40 mmzC = +3 mz2 = −3.5 mg = 9.81 m/s²patm = 101.3 kPa
pC = kPa
6.Hard
12d1​ = 150 mm, p1​ = 250 kPad2​ = 50 mm, p2​ = ?Δz = 7 m

Water flows up through a pipe that narrows from 150 mm to 50 mm while rising 7 m. At section 1 the pressure is 250 kPa and the velocity is 1 m/s. Ignoring losses, find the pressure p2 at section 2.

d1 = 150 mmd2 = 50 mmp1 = 250 kPav1 = 1 m/sΔz = 7 mρ = 1000 kg/m³
p2 = kPa

Answer key

  1. 1. Q = 22.09 L/s
  2. 2. v2 = 2.637 m/s
  3. 3. p2 = 189.7 kPa
  4. 4. p2 = 254.5 kPa
  5. 5. pC = 37.53 kPa
  6. 6. p2 = 141.3 kPa

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