Fluid Dynamics – Why Doesn’t a Hydraulic Lever Violate Conservation of Energy?

energy-conservationfluid dynamicsnewtonian-mechanicspressure

Suppose I apply some force on one side of hydraulic lift where area is less, and the fluid in the lift raises some heavier object on the other side where area is more. Now, work done is $\text{Force}\times \text{Displacement}$ and displacement on both side is same (incompressible liquid) but the force on one side is less, so we get more energy on other side. Then why doesn't the law of conservation of energy fail here?

Best Answer

enter image description here Displacement in both sides is not same. If on one side of lift the area is $A_1$, and on other side it is $A_2$, and we apply a force $F_1$ on one side to distance $d_1$ then volume decreased in one side is $=A_1 d_1$

Equal amount of volume will raise in the other side.

So $$A_1 d_1=A_2 d_2$$

$A_1 \not= A_2$, so $d_1 \not=d_2$.

Actually, we need to apply the little force $F_1$ for a greater distance $d_1$.

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