Stationary vane problem

Stationary vane problem

Consider a jet that is deflected by a stationary vane, such as is given in Fig. 11.4. If the jet speed and diameter are 25 m/s and 25 cm, respectively and jet is deflected 60⁰, what force is exerted by the jet on the vane?

Fig 11.4

First solve for F_x , the x-component of force of the vane on the jet -

Here, the final velocity in the x-direction is given as

Hence,

also,

and

Therefore,

similarly determined, the y-component of force on the jet is

Then the force on the vane will be the reactions to the forces of the vane on the jet, or