- #1
Saitama
- 4,243
- 93
Homework Statement
I don't have the exact problem statement but I remember the data given.
I have a cylinder suspended in mid-air.The question asks to calculate the wind speed required to keep the cylinder in this position. The cylinder is of height h and diameter d. The pressure of air is P and temperature is T. Molar mass of air M and density of cylinder is ##\rho##. Assume that the wind gust that keeps the cylinder suspended is blowing straight upwards, and that the air molecules bounce off the cylinder elastically.
Homework Equations
The Attempt at a Solution
I think I have to equate the lift force due to air with the weight of cylinder. The lift force is given by ##\frac{1}{2}\rho' v^2A## where ##\rho'## is density of air and A is the projected (or effective?) area.
Here, ##A=hd## and ##\rho'=\frac{PM}{RT}##. The weight of cylinder is ##\frac{(\pi d^2 h)\rho g}{4}##. Equating them
[tex]\frac{1}{2}\frac{PM}{RT} v^2 hd=\frac{(\pi d^2 h)\rho g}{4}[/tex]
Solving for v gives the wrong answer.
Any help is appreciated. Thanks!