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 = 23 L/sv = 1.5 m/s, d = ?

A water line must carry 23 L/s. To limit noise and wear, the mean velocity should be 1.5 m/s. Find the inner pipe diameter d needed.

Q = 23 L/sv = 1.5 m/s
d = mm
2.Easy
12d1​ = 150 mm, v1​ = 2.75 m/sd2​ = 75 mm, v2​ = ?

Water flows through a pipe that narrows from 150 mm to 75 mm in diameter. The velocity in the wide section is 2.75 m/s. Find the velocity v2 in the narrow section.

d1 = 150 mmd2 = 75 mmv1 = 2.75 m/s
v2 = m/s
3.Medium
12d1​ = 100 mm, p1​ = 280 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 280 kPa and the velocity is 2.5 m/s. Ignoring losses, find the pressure p2 in the narrow section.

d1 = 100 mmd2 = 75 mmp1 = 280 kPav1 = 2.5 m/sρ = 1000 kg/m³
p2 = kPa
4.Medium
12d1​ = 100 mm, p1​ = 400 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 400 kPa and the velocity is 0.75 m/s. Ignoring losses, find the pressure p2 in the narrow section.

d1 = 100 mmd2 = 75 mmp1 = 400 kPav1 = 0.75 m/sρ = 1000 kg/m³
p2 = kPa
5.Hard
C212.5 m4.5 md = 25 mmpC​ = ?

A hose with an inner diameter of 25 mm siphons water from an open tank. The highest point C of the hose is 2.5 m above the water surface, and the outlet (open to the air) is 4.5 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 = 25 mmzC = +2.5 mz2 = −4.5 mg = 9.81 m/s²patm = 101.3 kPa
pC = kPa
6.Hard
12d1​ = 150 mm, p1​ = 260 kPad2​ = 75 mm, p2​ = ?Δz = 2 m

Water flows up through a pipe that narrows from 150 mm to 75 mm while rising 2 m. At section 1 the pressure is 260 kPa and the velocity is 2.75 m/s. Ignoring losses, find the pressure p2 at section 2.

d1 = 150 mmd2 = 75 mmp1 = 260 kPav1 = 2.75 m/sΔz = 2 mρ = 1000 kg/m³
p2 = kPa

Answer key

  1. 1. d = 139.7 mm
  2. 2. v2 = 11 m/s
  3. 3. p2 = 273.2 kPa
  4. 4. p2 = 399.4 kPa
  5. 5. pC = 32.63 kPa
  6. 6. p2 = 183.7 kPa

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