Acertain hydraulic system is designed to exert a force 100 times as large as the one put into it. (a) what must be the ratio of the area of the cylinder that is being controlled to the area of the master cylinder? (b) what must be the ratio of their diameters? (c) by what factor is the distance through which the output force moves reduced relative to the distance through which the input force moves? assume no losses due to friction.

a)

b)

c)

Explanation:

Applying the Pascal principle:

Equation (1)

F: Force

A: Area

P: Pressure

Nomenclature:

Fp: Force on the primary piston

Fs: Force on the secondary piston

Ap: Primary piston area

As: Secondary piston area

a) Calculation of the relationship of areas:

The pressure acting on one side is transmitted to all the molecules of the liquid because the liquid is incompressible.

In the equation (1):

Pp = Ps

Equation(2)

We know that Fs = 100Fp, then we replace Fs in equation (2)

 We eliminate Fp, then:

Equation (3)

b)Calculation of the relationship of diameters (d)

In the Equation (3) we replace: ,

; we eliminate π

c) Reduction factor of the distance that the force moves at the exit (Ls) with respect to the distance that the force moves at the entrance (Lp):

The volume that moves at the entrance (Vp) is equal to the volume that moves at the exit (Vs).

Vp = Vs

Ap * Lp  = As * Ls  

, of the equation (3) then,