The flow in the impeller of a centrifugal pump is modeled by the superposition of a source and a free vortex. The impeller has an outer diameter of \(0.5 \mathrm{~m}\) and an inner diameter of \(0.3 \mathrm{~m}\). At the outlet from the impeller, the flowing water has the following velocity components, relative to the impeller: radial component \(2 \mathrm{~m} / \mathrm{s}\) and tangential component \(7 \mathrm{~m} / \mathrm{s}\).

(a) Find the strength of the source and the vortex required to model this flow.

(b) Assume that the impeller blades are shaped like the streamlines and plot an impeller blade shape.

(c) Find the radial and tangential components of velocity at the inlet to the impeller.