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Pascal’s Principle

Now that we have a general understanding of pressure, let’s dive into Pascal’s Principle. Essentially, when you apply pressure to one part of a fluid in a confined space, that pressure is transmitted undiminished to all other parts of the fluid. In technical terms, in a confined fluid, an external pressure applied to the fluid is distributed evenly throughout the fluid.

The foundational equation for this principle is:
\[ P_1 = P_2 \]
This implies:
\[ \frac{F_1}{A_1} = \frac{F_2}{A_2} \]

Relationship between Force and Area

While understanding the equation is important, it’s often more crucial to grasp the proportionality, especially for MCAT-style questions. So, let’s break down the relationship between force and area on the same side of a system.

Let’s consider two sides of a system, like in a hydraulic press. If one side (Side A) has a larger area than the other (Side B), and you apply the same pressure to both sides, the larger side (Side A) will experience a larger force. Why? Because for pressure to remain constant across both sides, the force has to change in proportion to the area.

Imagine doubling the area of Side A compared to Side B. To keep the pressure constant, the force on Side A has to be double that of Side B. In essence:
\[ F_A = 2 \times F_B \]
\[ A_A = 2 \times A_B \]

This doesn’t just apply to doubling though it applies to all sorts of factor changes. So if you half the area you would half the force and if you triple the area you got it you triple the force.

This principle is what makes hydraulic systems so powerful and useful. By adjusting the areas in a system, we can amplify forces, enabling us to do things like lifting cars with hydraulic jacks or operating heavy machinery.