You could write an integral, or just use excel to do a discrete sum. Since the elbow is simply an body of revolution about a fixed point in space, you summation will be something along the lines of the radius of the bend times a tapered cylinder.
The centroid of that "slice" will just be a function of theta (i.e [tex]\bar{x}=r\sin\theta\,\,\,\,\bar{y}=r\cos\theta[/tex]).