流体力学与 及传热课件Centrifugal pump theory.pptVIP

2.2.4.2 Centrifugal pump theory;In an ideal pump, liquid is assumed to flow through the unit without friction, and at any given cross section all to flow at the same velocity. As shown in the vector diagram for a single vane, Fig. This assumption in turn is equivalent to assumption that there are an infinite number of vanes, of zero thickness, at an infinitesimal distance apart.;The power input to the impeller, and therefore the power required by the pump, can be calculated from the angular-momentum equation for steady flow. ; Since work done per second N=Tω (ω angular velocity), the power equation for an ideal pump is (where α=90o,Vt1=0) ;Therefore, combining Eq(2.2-14) and Eq.(2.2-15) gives ;Since u2, A, and β2 are constant for a given rotating speed and a given size of the pump.; The equation is for a ideal pump. The plot of theoretical head H versus capacity Q is shown in figure. ; β2 90o are forward facing and Head increases with Q, ;Difference between Theoretical and Actual Head Developed ;The effects of speed on capacity, head and power - The Affinity Laws ; When the rotational speed n of a pump is increased, tip speed u2 rises proportionally; in an ideal pump velocity V2, Vt2, and Vr2 also increase directly with n. ; As rough approximations, the following relationships, called affinity laws, can be used for a given pump. ; The capacity Q is directly proportional to the rpm n. According to the equation 2.2-20 : ; The power consumed W is proportional to the product of H and Q, or; A given pump can be modified when needed for a different capacity by changing the impeller size. Then the affinity laws for a constant-rpm n are as follows: