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This idealized treatment is only a starting point. Further factors we consider while designing include the following:
On account of the considerable variation in the flow conditions and the blade section along the span, it is divided in to a number of infinitesimal section of small radial thickness dr. the flow through such a section is assumed to be independent of the flow through other elements.
Velocities is a blade force for the flow through the elemental section are shown below. The flow has a mean velocity w and direction b (from the axial direction). The lift force L is normal of mean flow and the drag D parallel to this. The axial (#Fx) and tangential (#Fy ) force acting on the element. Also (#Fr) is the resultant force inclined at an angle 0 to the direction of lift.
An expression for the pressure rise (#P) across the element is now developed.
Resolving the force in the axial and tangential direction,
#Fx = #L sinb - #D cosb
#Fy = #L cosb + #D sin b
By definition lift and drag force are
#L = ½ CL p w2 (ldr)
#D = ½ CD p w2 (ldr)
tanf = #D/#L = CD/CL
Since the fan laws are valid for any particular point on the fan pressure/volume characteristic, similar laws will be valid for every other point of operation, the only difference being numerical values of the coefficients. Thus a plot of Kp against Kq will have exactly same form as the pressure /volume characteristic of each fan in homologous series, and also be used to compare the performance of the series design with that of another series design. A system of performance coefficients based on this;
Application of Fan Engineering Formula:
The application of the fan theory can best shown by example.
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