Beth is studying a rotating flow in a wind tunnel She measur

Beth is studying a rotating flow in a wind tunnel. She measures the u and v components of velocity using a hot-wire anemometer. At x = 3.14 m and y = -2.44 m, u = 1.14 m/s and v = 3.2 m/s. Unfortunately, the data analysis program requires input in cylindrical coordinates (r, theta) and (u_r, u_theta). Help Beth transform her data into cylindrical coordinates. Specifically, calculate r, theta, u_r, and u_theta at the given data point.

Solution

We know, r² = x²+y²

Here, x= 3.14

         y= - 2.44

r= (3.14)² + (- 2.44)²

r = 15.81

tan = y/x

       = -2.44/3.14

tan = - 0.77

= 142.15 (Answer)