Final answer:
To determine the inlet vane angle of a centrifugal pump with specified dimensions and operating conditions, one would use velocity triangles and the conservation of angular momentum in fluid dynamics.
Step-by-step explanation:
The question is asking to determine the inlet vane angle of a centrifugal pump based on given specifications and assumptions. The pump has an external diameter of 450 mm, an internal diameter of 200 mm, and operates at 1440 r.p.m with a constant radial flow of 2.5 m/s. Additionally, the pump's vanes at the exit are set back at an angle of 25 degrees.
To find the inlet vane angle, we must consider the velocity triangles associated with the pump impeller's motions and make use of the principle of conservation of angular momentum for a particle in circular motion, with adjustments for the fluid dynamics in the pump.
While the question does not provide sufficient information directly to calculate the inlet vane angle, the process typically involves using the tangential velocity component of the impeller at the inlet, which can be calculated using the impeller's speed and internal diameter, and the given radial flow velocity.