Transmission of Pressure through an Enclosed Liquid (Pure Only)

1. Force $F_1$ is applied on piston 1 Pressure exerted on piston 1 and hence the liquid is $P_1=\frac{F_1}{A_1}$ where $A_1$ is the area of piston 1. This is equation 1

2. As liquid cannot be compressed, pressure $P_1$ would be transmitted equally(undiminished) to other parts of the liquid and to piston 2

3. pressure exerted on piston 2 is $P_1=\frac{F_2}{A_2}$, where $F_2$ is the force on piston 2 and $A_2$ is the area of piston 2. this is equation 2. Substitute equation 1 into 2: $\frac{F_1}{A_1}=\frac{F_2}{A_2}$ $\cdot$ $F_2{A}_1$ = $F_1{A}_2$ $F_2$ = $F_1\frac{A_2}{A_1}$

since $A_2$ is much larger than $A_1$, force $F_2$ is much larger than $F_1$

Final Formula $F_2=F_1\frac{A_2}{A_1}$

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$F_2$ is a multiple of $F_1$. Multiple is given by the ratio of areas of $A_2$ to $A_1$ Thus, hydraulic press has a multiplier effect (proportional increase Converts relatively small force ($F_1$) on a small piston into a relatively large force $F_2$ on a large piston

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Example Question Explain why hydraulic press would not work if liquid contains bubbles of air

• bubbles of air are compressed when piston is pushed. Leads to a shorter distance moved by other piston as the pressure on piston X would not be equally transmitted to all parts of the liquid. Force applied would be used to compress bubbles of air as well. thus, lesser pressure is applied on the piston, which leads to a smaller force applied on larger piston. This means hydraulic system will not work Efficiently

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Related topic: Pascals principle or Pascals Law:

Definition

if pressure applied to an enclosed liquid, pressure is transmitted to all other parts of the liquid undiminished.

• this is multiplier effect of hydraulic press. #PhysicsDefinitions Pascals Principle or Pascals law

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