Question

What is the minimum diameter at section (1) in the pipe below to avoid cavitation at that location? Take D2= 15 cm. Neglect friction head loss in the pipe. (3) Water 5 m (1) (2)

Answer 1

The minimum diameter at section (1) in the pipe below to avoid cavitation at the location is 16.6 cm.

Look at the picture

• In section (1) according to Torricelli's law the speed of water
  v² = 2gh
  h = the height of fluid above the opening = 5 m
  g = acceleration due to gravity = 9.8 m/s²
  v² = 2gh = 2 × 9.8 × 5 = 196 $v = \sqrt{196}$
  v = 14 m/s
• The preassure in section (1)
  p₁ = p atm + p hidrostatic
  p₁ = 1.01 × 10⁵ + ρgh
  p₁ = 1.01 × 10⁵ + (1,000 × 9.8 × 5)
  p₁ = 1.01 × 10⁵ + 49,000
  p₁ = 1.5 × 10⁵ Pascal
• The pressure in section (2) equals atmosphere pressure because it is connected to open air.
  p₂ = p atm = 1.01 × 10⁵ Pascal

According to Bernoulli's equation in sections (1) and (2)

p₁ + 0.5 ρv₁² = p₂ + 0.5 ρv₂²

1.5 × 10⁵ + (0.5 × 1,000 × 14²) = 1.01 × 10⁵ + (0.5 × 1,000 × v₂²)

1.5 × 10⁵ - 1.01 × 10⁵ + 98,000 = 500 × v₂²

49,000 + 98,000 = 500 × v₂²

147,000 = 500 × v₂²

v₂² = 147,000 ÷ 500

v₂² = 294

$v_2 = \sqrt{294}$

v₂ = 17.15 m/s

According to the continuity equation for fluids

A₁ v₁ = A₂ v₂

$\frac{1}{4} D_1^2 v_1 = \frac{1}{4} D_2^2 v_2$

D₁² v₁ = D₂² v₂

D₁² × 14 = 15² × 17.15

D₁² = 3,858.75 ÷ 14

D₁² = 275.625

$D_1 = \sqrt{275.625}$

D₁ = 16.6 cm

Learn more about Bernoulli equation here: https://brainly.com/question/26761275

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