For laminar flow in circular pipe the ratio of net power input to volume varies as _______ (where, R = radius of circular pipe)
- A1/R
- B1/R²Correct
- C1/R³
- DR²
Solution
Concept
Power per unit volume
Formula
P/V = (Δp/L) V̄ = 8μV̄²/R²
Step-by-step solution
1. Δp/L = 8μV̄/R² for Hagen–Poiseuille flow. 2. Power per unit volume = (Δp/L) V̄ = 8μV̄²/R². 3. For a given mean velocity it varies as 1/R².
Explanation
The shear dissipation per volume falls with the square of the radius.
Shortcut
P/V ∝ 1/R².
Correct answer: B) 1/R²