For ideal flow (no friction) the velocity V_1 around the surface of a long cylin

Question

For ideal flow (no friction) the velocity V_1 around the surface of a long cylinder is given by V_1 = 2 V_0 sin theta where V_0 is the free stream velocity and theta the angular location around the cylinder measured from the front (stagnation point). Consider a concrete chimney 20 m in diameter and 275 m in height subject to a wind velocity of 100 km/h. Determine the velocity and pressure of the air on the front (stagnation point - point 1) and sides (90 degree from stagnation point - point 2) of the chimney. Express the pressure relative to atmospheric pressure (gauge pressure).

Explanation / Answer

GIVEN:- Diameter D of chimney = 20m, Height of chimney H = 275m, Free wind velocity Vo = 100km/h = 27.8m/s

SOLUTION:-

= 0 for point-1 & = 90 for point-2

By formula V1 = 2 x Vo x Sin(0) = 2 x 27.8 x Sin(0) = 0 m/s & P1 = 0.00256 x V1^2 = 0.00256 x 0 = 0

So Velocity & Pressure at point-1 = 0m/s & 0 Pa (ANSWER)

Again, V2 = 2 x Vo x Sin(90) = 2 x 27.8 x 1 = 55.6 m/s & P2 = 0.00256 x V2^2 = 0.00256 x 55.6^2 = 7.91

So Velocity & Pressure at point-2 = 55.6m/s= 200 km/h & 7.91 Pa (ANSWER)

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