The diameter of pipe at section (1) and (2) are 10 and 15 cm respectively.

Question

1. The diameter of pipe at section (1) and (2) are 10 and 15 cm respectively. Find discharge through pipe if the velocity of water flowing through pipe at section (1) is 5 m/s. Find also velocity at section (2) 

2. Find the work done in blowing a soup bubble of surface tension 0.06 N/m from a 2 cm radius to a 5 cm radius.

Answer 1

1.

Q = A₁V₁ = π × \(\frac{0.1^2}{4}\) × 5

= 0.0393 m³ /s

V₂ = \(\frac{A_1V_1}{A_2}\) (continuity equation)

= 2.22 m/s

2. Here, s = 0.06 N/m

r₁ = 2 cm = 0.02 m ;

r₂ = 5 cm = 0.05 m

Since bubble has 2 surfaces, initial surface area of the bubble.

= 2 × \(4πr_1^2\)= 2 × 4π(0.02)²

= 32π × 10^-4m²

Final surface area of the bubble

= 2 × \(4πr_2^2\) = 2 × 4π(0.05)²

= 200π × 10^-4m²

Increase in surface area

= 200π × 10^-4 – 32π × 10^-4

= 168π × 10^-4m²

∴ work done = S × increase in surface area

= 0.06 × 168π × 10^-4 = 0.003168 J