## W dm

Vmo is the local meridional velocity component neglecting blockage. (One-dimension-ally, Vm o is the value of Vm found from Eq. 16, where the radius r is that from the axis of rotation to the center of the circle of diameter b in Figure 8, which in turn lies on an imaginary line in Figure 8 that is normal to the hub, shroud, and intermediate stream surfaces.) Here, AWb emerges by applying Bernoulli's equation [Eq. 21 with no change in radius (that is, no change in U) or loss as one traverses from pressure side to suction side of the passage] to the static pressure difference pp — ps arising from the delivery of angular momentum to the fluid (Eq. 26). This in turn results from the application of the shaft torque to the blades. It is also assumed in the derivation of Eq. 54 that the blade-to-blade average relative velocity W lies halfway between the surface velocities Ws and Wp, (which would exist just outside the boundary layers on the blades,) as illustrated in Figure 17. This is a good assumption for efficient flow well within a bladed channel22. AWb is inversely proportional to the solidity because, on the average, from inlet to outlet, Eq. 54 becomes

where it can be seen from Figure 16 and Eq. 53 that the fraction involving the number of blades nb is the reciprocal of the solidity s because

For unconventional impeller geometries, the foregoing solidity guidelines may be inadequate to assure efficient flow. For any geometry, though, the concept of a diffusion factor D, utilized by NACA researchers23 to assess stationary cascades of airfoils can be employed. In view of Eqs. 53—56, their equation for D takes the following form for both axial- and non-axial-flow geometries, rotating or not:

This can be deduced from Figure 17 as follows:

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