The polar angle of a variable point defining the trajectory of a fluid particle in a centrifugal impeller is obtained using mechanics of particles in a rotating coordinate system. The expression for the angle then yielded the impeller outlet relative flow angle, which was used to calculate slip factor. An attempt to explain the phenomenon of slip using an oblique coordinate system with axes in the direction of the tangent to a vane and in the tangential direction then enabled a new expression for slip factor to be obtained. The computed values of slip factor using available pump data compare reasonably well with reference values.
The paper presents a basis for teaching centrifugal pump characteristics in an undergraduate course in turbomachinery. It is shown how the shock and frictional loss coefficients, key factors in the determination of pump characteristics, can be appropriately obtained. The first coefficient is obtained from the difference between the drag at a reference incidence and that at zero incidence, while the second is obtained from correlations for frictional loss in a spiral. The coefficients so obtained were used to obtain the real characteristics of a centrifugal pump impeller.
Using the equation of motion of a particle in a rotating co-ordinate system, it is shown that the head developed and the power required by a centrifugal pump are uniquely obtained from centrifugal forces. An expression is then obtained for the optimum outlet blade angle which is used to demonstrate that the phenomenon of slip has a dynamical basis.
A new expression is developed for the optimum outlet blade angle of a HAWT turbine blade element using impulse turbine theory. A simple numerical scheme is then given for calculating the blade angle using a modified expression for the relative velocity coefficient. Numerical results are presented which are in good agreement with optimum values.
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