The theory of turbines

Robert H. Thurston
1884 Journal of the Franklin Institute
Concluded from page 459.) 24. Centrifilgal action and friction modify the theory of the turbine, as already indicated; the one altering~ in equal amount, both the energy expended and the energy usefully applied, and the other by reducing the head, reaching and impelling tile wheel. It has been seen that these quantities of work can be represented by expressions involving the velocities of current and quantities having the forms f(n) = Nandf(f) = .F~ in which n is the value of ~" andf is a
more » ... ~" andf is a funcrl tion of the coefficient of fluid friction. Values of N have been giveu in Tables I-IV, ibr various values of ho, the head due centrifugal action, and those of f(f) are easily calculated when the elements and action of the wheel are given. The expressions for head and efficiency then become, for the first form of wheel, friction included. h, --Z"~ --~':~ + 1 (2 ar~v~ --a~,',:~) = Nv} (62)' 2g 1 (n~v~ sec" 2 fl + 2at,v,-aZrl 2 --_Nv, 2 @ Fv,') (63) E=-(n~ + 1) (2arv,--a~r}) -Nv~ ~ (64) n~v~ 2 sec} fl + 2arv 1 ~ a2r, ~-Nv, 2 + Fvl 2 " When v 1 : ar~ ; v2 ~ nar~ = nv~ , /~, = n 2 q-1 --N ; (65} n2 sec.2fl + 1 --N+ F when n = 1, E= 2--N (66) see.2fl + 1--N+F and when flo, ~2 E---4-1 --N (67) n2+I~N+F ' which becomes unity when/~' becomes o. The magnitude of the quantity N which appears in the completed equations for efficiency and head may now be readily determined for the. cases studied~ It. is not" as is. easily s.hown, the value of' f(n),