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JEE Advanced Physics Mechanical Properties of Fluids 2023 JEE Advanced 2023 (Paper 2)

JEE Advanced Physics Question (2023) — Solution

Question

A cylindrical furnace has height H and diameter D both 1   m . It is maintained at temperature 360   K . The air gets heated inside the furnace at constant pressure  P a  and its temperature becomes T = 360   K . The hot air with density ρ  rises up a vertical chimney of diameter d = 0 . 1   m and height h = 9   m above the furnace and exits the chimney (see the figure). As a result, atmospheric air of density  ρ a = 1 . 2   kg   m - 3 , pressure P a  and temperature T a = 300   K enters the furnace. Assume air as an ideal gas, neglect the variations in  ρ  and T inside the chimney and the furnace. Also ignore the viscous effects. [Given: The acceleration due to gravity  g = 10   m   s - 2  and  π = 3 . 14 ] Considering the air flow to be streamline, the steady mass flow rate of air exiting the chimney is _____ gm   s − 1 .

Options

  1. A. A
  2. B. B
  3. C. C
  4. D. D

Answer

A. A

Step-by-step solution

Applying Bernoulli’s theorem between top and bottom points of furnace : P a + 1 2 ρ a V 2 = P a + ρ g H + 1 2 ρ V 2                                 . . .   1 Also, since  P M = ρ R T ⇒   ρ a × 300 = ρ × 360 ⇒   ρ = 1   kg   m - 3                           . . .   2 From equation(1), we can write ⇒   V 2 2 0 . 2 = 1 × 10 × 1 ⇒   V = 10   m   s - 1 Required mass flow rate  = V × π D 2 4 × ρ = 10 × 3 . 14 4 × 1 2 × 1   kg   s - 1 = 7 . 85   kg   s - 1 = 7850   gm   s - 1

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Related: Physics — Mechanical Properties of Fluids · All PYQ Banks