Explanation Given information: Diameter of rain droplet = 100 m/min Temperature = 25 degree Celsius The given condition is that the rain droplet is suspended in air. For this there must be some force applied by air to the rain droplet to overcome the weight of rain droplet. The resultant force will be equal to the sum of buoyancy force and force exerted by air. The equilibrium exists if the upward force is equal to downward force. For air at T = 25°C: ρ = 1 .184 kg/m 3 μ = 1 .849 × 10 -5 For water at 25°C: ρ = 997 .0 kg/m 3 Now, using data from the textbook, The value of downward force is given by using the given formula, F down = π D 3 6 ρ raindrop g The upward force includes air drag force and force exerted by the water i.e., buoyancy force. F up = 3 π μ V D + π D 3 6 ρ air g So, after solving the above equations, we get, downward force = upwards force i.e., ⇒ F down = F up ⇒ π D 3 6 ρ raindrop g = 3πμVD + π D 3 6 ρ air g ⇒ π D 3 6 ( ρ raindrop -ρ air ) g = 3πμVD Now, solving the equation for the velocity of air

Fluid Mechanics: Fundamentals and Applications

4th Edition

ISBN: 9781259696534

Author: Yunus A. Cengel Dr., John M. Cimbala

Publisher: McGraw-Hill Education

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Chapter 10, Problem 24P

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Fluid Mechanics: Fundamentals and Applications

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The vertical speed of air to keep raindrop suspended in air.

Solution Summary: The author explains the vertical speed of air to keep raindrop suspended in air is 0.097 m/s. The resultant force is equal to the sum of buoyancy force and force exerted by air.

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