Consider steady, incompressible flow maintained between two concentric cylinders by steady angular velocity of both cylinders. Let the inner cylinder have radius r0, angular velocity w0, and the outer cylinder has r1 and w1, respectively. Assume that there is no axial velocity and gravitational effect is negligible. Make appropriate assumptions if necessary. clearance (h = r1-r0) is NOT small. (Note: This was the problem of the final exam in 2014) (a) Derive an expression for the tangential velocity profile of the fluid between two cylinders. State all the assumptions that are necessary to reduce the governing equations (continuity and Navier-Stokes equations) you choose. Please indicate what assumptions are used to eliminate of the terms in the equation. State appropriate boundary conditions. (b) Determine the velocity profile in the limit as the outer cylinder becomes very large and remains fixed (r1 right arrow infinite, w1= 0).

initial speed when it is dropped is 150 ft/s

now at the same moment the acceleration due to gravity is perpendicular to its velocity

so as we know that

now we have centripetal acceleration a = 32 ft/s^2 as its perpendicular to velocity

while tangential acceleration at the same moment will be zero

so

now radius of curvature is given as

so the radius of curvature just after it is dropped is 703.125 ft

the design of a ski jumping suit involves a trade-off between giving the skiers lift to get higher jumps and ensuring the skier does not face a lot of drag before the jump itself. an expansive suit may to lift the skier higher, but at the same time, it will also increase the air resistance. higher air resistance as the skier goes down the slope limits the speed of the jump. a big suit also increases the risk of losing balance or control, especially if there's a strong gust of wind. while technologically enhanced suits a lot, clothing is not the only factor in a ski jumper’s success. gathering speed while skiing down the slope, ensuring good speed on the ramp, and maintaining good body posture and form in the air all contribute to a ski jumper's success.

365.25 earth days are in the year of a light year