Question

Water flows through a horizontal tube as shown in figure (13-E9). If the difference of heights of the water column in the vertical tubes is 2 cm, and the areas of the cross-section at A and B are 4 cm² and 2 cm² respectively. Find the rate of flow of water across any section

Answer 1

Given,

Area of the cross-section A = 4 cm²,

Area of the cross-section B = 2 cm².

Volume rate of flow = Area × velocity

V = 4v₁ = 2v₂

Using the Bernoulli's theorem,

 P₁ + h₁ρg + 1/2ρv₁² = P₂ + h₂ρg + 1/2ρv₂²

Now, Pipe is horizontal, therefore,

   P₁ + 1/2ρv₁² = P₂ +  1/2ρv₂²

  P₁ - P₂ = 1/2 ρ(v₂² - v₁²)

  hρg = ρ(v₂² - v₁²)/2

  2hg = (v₂² - v₁²)

  2 × 2 × 980 = V²/16 - V²/4

 4 × 980 = 3V²/16

V² = 64 × 980/3

V = 144.59 cm³/seconds.

Hence, the volume rate of flow is 144.59 cm³/seconds.

Hope it helps.

Answer 2

Answer:

Please Refer to the above attachment.

Thank you!