Show that the mechanical advantage of a hydraulic press is greater than one.

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Solution

The mechanical advantage of the hydraulic press:-
$M . A = \frac{T h r u s t g e n e r a t e d}{E f f o r t a p p l i e d}$
$M . A .$ = $M e c h a n i c a l a d v a n t a g e o f t h e l e v e r \times \frac{C r o s s - s e c t i o n o f p r e s s p l u n g e r}{C r o s s - s e c t i o n o f p u m p p l u n g e r}$
$M . A . = (A q u a n t i t y g r e a t e r t h a n 1 \times \frac{π {(R a d i u s o f p r e s s p l u n g e r)}^{2}}{π {(R a d i u s o f p u m p p l u n g e r)}^{2}} M . A . = (> 1) \times {(\frac{R a d i u s o f p r e s s p l u n g e r}{R a d i u s o f p u m p p l u n g e r})}^{2}$
The ratio of the radius of the press plunger to that of the pump plunger is greater than one.
Therefore, mechanical advantage do hydraulic press, $M . A . > > 1$ .

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