Your question is kind of vague..... is this part of some type of homework assignment ??
Pump shafts are typically "stepped shafts" ( various diameters) that are provided by the manufacturer and designed for the specific application. Commonly, they are machined from carbon steel (SAE4140 is typical) but stainless is also offered at a premium price. Pump shafts are designed to take the maximum torque and bending loads of the pump at extreme conditions with minimum deflection.
Limiting deflection of a pump shaft is important to ensure that mechanical seals have a long life. ASME/ANSI B73.1 is a standard widely used in the industry. This standard establishes a group of specific pump sizes and limits pump deflection (to .002" at seal faces) during operation. Limiting deflection is accomplished by the pump vendor by using larger diameter shafts
See the "Pump Handbook" by Karassik for more info.......
Hope that this helps..............................MJC