In a hydraulic press, the small cylinder has a diameter of d 1 cm, while the large cylinder has a diameter of d 2 cm. If a force F 1 is applied to a piston of small cylinder, then the force on t

Question

In a hydraulic press, the small cylinder has a diameter of d 1 ​ cm, while the large cylinder has a diameter of d 2 ​ cm. If a force F 1 ​ is applied to a piston of small cylinder, then the force on the piston of large cylinder F 2 ​ is

TestHub · Accepted Answer

According to Pascal's law, the pressure is transmitted equally in all directions in an enclosed fluid.

Pressure on the small cylinder is $P_{1} = \frac{F _{1}}{A _{1}}$

Pressure on the large cylinder is $P_{2} = \frac{F _{2}}{A _{2}}$

Equating the pressures, $P_{1} = P_{2}$

$\frac{F _{1}}{A _{1}} = \frac{F _{2}}{A _{2}}$

The areas of the cylinders are $A_{1} = \frac{π d _{1}^{2}}{4}$ and $A_{2} = \frac{π d _{2}^{2}}{4}$

Substituting the areas into the equation:

$\frac{F _{1}}{\frac{π d _{1}^{2}}{4}} = \frac{F _{2}}{\frac{π d _{2}^{2}}{4}}$

$\frac{F _{1}}{d _{1}^{2}} = \frac{F _{2}}{d _{2}^{2}}$

$F_{2} = \frac{d _{2}^{2}}{d _{1}^{2}} F_{1}$

Answer: $\frac{d _{2}^{2}}{d _{1}^{2}} F_{1}$

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