Usefulness of the Calculator

This Pascal’s Law Calculator is an essential tool for students, engineers, and technicians working with hydraulic systems. It allows for the rapid calculation of any unknown variable (force or area) in a closed hydraulic system, provided the other three values are known. This is crucial for:

• Designing Hydraulic Jacks: Determining the necessary input force ($F_1$) to lift a heavy load ($F_2$).
• Sizing Pistons: Calculating the required area ($A_2$) of the output piston to achieve a desired output force.
• Verification: Quickly checking the theoretical performance of an existing hydraulic setup.

The Main Formula

Pascal’s Law states that pressure exerted anywhere in a confined incompressible fluid is transmitted equally in all directions throughout the fluid such that the pressure ratio remains constant. Mathematically, this is expressed as: $$ \frac{F_1}{A_1} = \frac{F_2}{A_2} $$

Where:

• $F_1$ = applied force (e.g., Newtons, N)
• $A_1$ = applied area (e.g., square meters, $m^2$)
• $F_2$ = transmitted force (e.g., Newtons, N)
• $A_2$ = transmitted area (e.g., square meters, $m^2$)

Step-by-Step Instructions

1. Identify Knowns: Determine which three of the four variables ($F_1$, $A_1$, $F_2$, $A_2$) you know.
2. Enter Values: Input the numerical values for the three known variables into their corresponding fields in the calculator above. The units must be consistent (e.g., Newtons for force, and $m^2$ or $cm^2$ for area, but you must use the same unit for both $A_1$ and $A_2$).
3. Leave One Field Blank: Crucially, leave only the field for the unknown variable empty.
4. Calculate: Click the Calculate Unknown Value button.
5. Review Result: The result will appear in the Results section, showing the calculated value for the missing variable and the formula used to find it.