By choosing values of the work coefficient at two radii, the values of a and b can then be found….
By choosing values of the work coefficient at two radii, the values of a and b can then be found. Let ψ 5 ψm 5 0:3 at the root mean square radius, r 5 rm 5 ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ð1=2Þðr2 h 1 r2 t Þ p and ψ 5 ψh 5 0:6 at r 5 rh. The values of the hub-to-tip radius ratio are rh=rt 5 0:4, rm=rt 5 0:7616, and rt 5 0:5 m. These choices of rh and rt and the values of the work coefficients are quite arbitrary and other values could be selected by the designer. Also, for use later, assume the local flow coefficient, φm 5 cxm=Um 5 0:5 and the rotational speed, Ω 5 500 rad=s. By substitution into the above equation for work coefficient, it is possible to evaluate a and b as a 5 8:286 and b 5 92:86