Fluid Mechanics Cheat Sheet

The core ideas of Fluid Mechanics distilled into a single, scannable reference — perfect for review or quick lookup.

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Quick Reference

Pressure

Force per unit area: P = F/A. In a fluid at rest, pressure acts equally in all directions at a given depth. Pressure increases with depth in a fluid: P = P_0 + rho*g*h. SI unit: pascal (Pa) = N/m^2.

Pascal's Principle

Pressure applied to an enclosed fluid is transmitted undiminished to every portion of the fluid and to the walls of the container. This enables hydraulic force multiplication: F1/A1 = F2/A2.

Archimedes' Principle

Any object wholly or partially submerged in a fluid experiences a buoyant force equal to the weight of the fluid displaced: F_b = rho_fluid * V_displaced * g.

Buoyant Force

The net upward force exerted by a fluid on an immersed object, caused by the pressure difference between the bottom and top of the object. Equal to the weight of displaced fluid.

Continuity Equation

For an incompressible fluid flowing through a pipe, the product of cross-sectional area and flow velocity is constant: A1*v1 = A2*v2. This is conservation of mass for fluids.

Bernoulli's Equation

For an ideal, incompressible fluid flowing along a streamline: P + (1/2)*rho*v^2 + rho*g*h = constant. This is conservation of energy per unit volume for fluids. Where speed is high, pressure is low.

Gauge Pressure vs. Absolute Pressure

Absolute pressure is the total pressure including atmospheric. Gauge pressure is the pressure above atmospheric: P_gauge = P_absolute - P_atm. Many instruments (tire gauges, blood pressure cuffs) measure gauge pressure.

Viscosity

A measure of a fluid's internal resistance to flow. High-viscosity fluids (honey, motor oil) flow slowly; low-viscosity fluids (water, air) flow easily. Viscosity causes energy dissipation in real fluid flow.

Flow Rate

The volume of fluid passing a point per unit time: Q = A*v, where A is the cross-sectional area and v is the flow velocity. SI unit: m^3/s.

Key Terms at a Glance

Pressure:Force per unit area: P = F/A. In fluids, pressure acts equally in all directions at a given depth. SI unit: pascal (Pa).

Pascal's Principle:Pressure applied to a confined, incompressible fluid is transmitted undiminished to every part of the fluid.

Archimedes' Principle:Buoyant force equals the weight of the displaced fluid: F_b = rho_fluid * V_displaced * g.

Buoyant Force:Net upward force on a submerged object due to fluid pressure differences. Equals weight of displaced fluid.

Continuity Equation:A1*v1 = A2*v2. Conservation of mass for incompressible fluid flow. Flow rate Q = Av is constant.

Bernoulli's Equation:P + (1/2)*rho*v^2 + rho*g*h = constant along a streamline. Energy conservation for ideal fluid flow.

Gauge Pressure:Pressure relative to atmospheric: P_gauge = P_absolute - P_atm. Can be positive, negative, or zero.

Absolute Pressure:Total pressure including atmospheric: P_absolute = P_gauge + P_atm. Always positive.

Flow Rate:Volume of fluid passing a point per unit time: Q = A * v. SI unit: m^3/s.

Viscosity:A fluid's internal resistance to flow. Causes energy dissipation. High viscosity: honey. Low viscosity: water.

Hydrostatic Paradox:Pressure at a depth depends only on depth, not on the shape or volume of the container.

Streamline:A line tangent to the velocity of the fluid at every point. Bernoulli's equation applies along a streamline.

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