Force Cheatsheet

Cheatsheet Content

Definition of Pressure Pressure ($P$) is defined as the force ($F$) applied perpendicular to a surface divided by the area ($A$) over which the force is distributed. Formula: $P = \frac{F}{A}$ Unit: Pascal (Pa), where $1 \text{ Pa} = 1 \text{ N/m}^2$. Other common units include psi (pounds per square inch), atm (atmosphere), bar, mmHg (millimeters of mercury), torr. Pressure is a scalar quantity. Types of Pressure 1. Absolute Pressure ($P_{abs}$) Measured relative to a perfect vacuum (zero pressure). Always positive. 2. Gauge Pressure ($P_{gauge}$) Measured relative to the local atmospheric pressure. Can be positive (above atmospheric) or negative (below atmospheric, i.e., vacuum). Relationship: $P_{abs} = P_{gauge} + P_{atm}$ 3. Atmospheric Pressure ($P_{atm}$) The pressure exerted by the weight of the atmosphere. Standard atmospheric pressure at sea level: $1 \text{ atm} = 101325 \text{ Pa} \approx 101.3 \text{ kPa}$ $1 \text{ atm} = 1.01325 \text{ bar}$ $1 \text{ atm} = 760 \text{ mmHg} = 760 \text{ torr}$ $1 \text{ atm} \approx 14.7 \text{ psi}$ Pressure in Fluids (Hydrostatic Pressure) Pressure exerted by a fluid at rest due to gravity. Formula for pressure at a certain depth ($h$): $P = \rho gh$ Where: $\rho$ (rho) is the density of the fluid (kg/m$^3$) $g$ is the acceleration due to gravity (approx. $9.8 \text{ m/s}^2$) $h$ is the depth from the surface of the fluid (m) Total absolute pressure at depth $h$: $P_{abs} = P_{atm} + \rho gh$ Key Properties: Pressure increases with depth. Pressure is the same at any given horizontal level in a continuous fluid. Pressure acts equally in all directions at a given point in a fluid. Pascal's Principle A pressure change at any point in a confined incompressible fluid is transmitted throughout the fluid such that the same change occurs everywhere. Application: Hydraulic systems (e.g., hydraulic lift). $P_1 = P_2 \Rightarrow \frac{F_1}{A_1} = \frac{F_2}{A_2}$ A small force ($F_1$) applied over a small area ($A_1$) can generate a large force ($F_2$) over a large area ($A_2$). Archimedes' Principle (Buoyancy) When an object is submerged (partially or fully) in a fluid, it experiences an upward buoyant force ($F_B$) equal to the weight of the fluid displaced by the object. Formula: $F_B = \rho_f V_{disp} g$ Where: $\rho_f$ is the density of the fluid $V_{disp}$ is the volume of the fluid displaced by the object $g$ is the acceleration due to gravity Object floats if $F_B \ge W_{object}$. Object sinks if $F_B Bernoulli's Principle (Fluid Dynamics) For an incompressible, non-viscous fluid in steady flow, the sum of pressure, kinetic energy per unit volume, and potential energy per unit volume is constant along a streamline. Formula: $P + \frac{1}{2}\rho v^2 + \rho gh = \text{constant}$ Where: $P$ is the static pressure $\frac{1}{2}\rho v^2$ is the dynamic pressure (kinetic energy per unit volume) $\rho gh$ is the hydrostatic pressure (potential energy per unit volume) $v$ is the fluid velocity Implication: Where fluid velocity is high, pressure is low, and vice versa (for horizontal flow). Measurement of Pressure Barometer: Measures atmospheric pressure. (e.g., Mercury barometer: $P_{atm} = \rho_{Hg} g h$) Manometer: Measures gauge pressure of a fluid. Open-tube manometer: $P_{gauge} = \rho g h$ Closed-tube manometer: Measures absolute pressure. Pressure Gauges: Various mechanical or electronic devices (e.g., Bourdon gauge, diaphragm gauge). Vapor Pressure The pressure exerted by a vapor in thermodynamic equilibrium with its condensed phases (solid or liquid) at a given temperature in a closed system. Increases with temperature. Boiling occurs when vapor pressure equals external pressure.