Final answer:
Calculations for a single-sided impeller involve determining the blade inlet angle using the velocity triangle, and the Mach number by comparing the tip velocity to the speed of sound in the fluid. Additional information is required for precise calculations, such as density and fluid velocity.
Step-by-step explanation:
The question involves calculating the blade inlet angle and the Mach number at the tip of the impeller eye for a single-sided impeller in a fluid dynamics context. The blade inlet angle can be determined using the velocity triangle which combines the impeller speed with the flow velocity of the fluid, while accounting for the radii at the root and the tip. The Mach number is a dimensionless quantity that describes the speed of an object moving through a fluid (or the speed of the fluid) divided by the speed of sound in that fluid. It's pertinent in applications of aerodynamics and engineering related to gases.
To calculate the blade inlet angle, you would typically need additional information such as the velocity of the fluid entering the blades (velocity triangle), which can be deduced from the mass flow rate and the density of the fluid (continuity equation).
To determine the Mach number at the tip of the impeller eye, you can first find the tip velocity of the impeller using its radius and rotation speed, and then compare this to the speed of sound in the fluid at the given ambient conditions (thermodynamic equations and the definition of Mach number).