Lecture 10

The degree of reaction

(10.3)

With the help of Eq. (10.2), it becomes

and

 

By adding up Eq. (9.1) and Eq. (9.2) we get

Replacing and in the expression for with and ,

 
(10.4)

As the case of 50% reaction blading is important in design, it is of interest to see the result for Λ =0.5 ,

and it follows from Eqs. (9.1) and (9.2) that

i.e.
(10.5a)
i.e.
(10.5b)

Furthermore since is constant through the stage.

And since we have initially assumed that , it follows that . Because of this equality of angles, namely, and , blading designed on this basis is sometimes referred to as symmetrical blading .The 50% reaction stage is called a repeating stage.

It is to be remembered that in deriving Eq. (10.4) for , we have implicitly assumed a work done factor of unity in making use of Eq. (10.2). A stage designed with symmetrical blading is referred to as 50% reaction stage, although will differ slightly for λ.