Pressure

• Pressure is a physical quantity (scalar) that measures the force applied perpendicular to the surface of an object per unit area

$P=\frac{F}{A}$

• $P$ is the pressure
• $F$ is the force applied
• $A$ is the area of the surface

todo https://physics.stackexchange.com/questions/429998/if-force-is-a-vector-then-why-is-pressure-a-scalar

Units

• (Pascal) $1\mathrm{Pa}=1\frac{\mathrm{N}}{{\mathrm{m}}^2}=1\frac{\mathrm{kg}}{\mathrm{m}\cdot {\mathrm{s}}^2}=1\frac{\mathrm{J}}{{\mathrm{m}}^3}$
• (Atmosphere) $1\text{atm}=101325\text{Pa}$ (roughly equivalent to the mean sea-level atmospheric pressure on Earth)
• $1\text{Torr}=133.322\text{Pa}$
• $1\text{Bar}=10^5\text{Pa}$

Pascal’s Law

• Pascal’s Law states that a change in pressure at any point in an enclosed incompressible fluid at rest is transmitted equally and undiminished to all points in all directions throughout the fluid, and the force due to the pressure acts at right angles to the enclosing walls.

$P_1=P_2$

• Where $P_1$ and $P_2$ are the pressures at two different points in a confined fluid

Hydraulic Press

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

• $A_1$ and $A_2$ are the areas of the small and large pistons, respectively
• $F_1$ is the force applied on the small piston
• $F_2$ is the force exerted by the large piston

$F_2=F_1\times \frac{A_2}{A_1}$

Work and Energy Conservation

$W_1=F_1\times d_1$ $W_2=F_2\times d_2$

• (input work) $W_1$ is the work done on the small piston
• (output work) $W_2$ is the work done by the large piston
• $d_1$ and $d_2$ are the distances moved by the small and large pistons, respectively

Conservation of Work

$F_1\times d_1=F_2\times d_2$ $W_1=W_2$