Fluids Exam Notes

Fluids

Definition of a Fluid

• Fluids are substances that have no fixed shape.
• Generally, liquids and gases are considered fluids.
• Fluids can flow easily.

Density

• Density is the degree of compactness of a substance.
• The symbol for density is ρ (rho).
• The formula for density is: density = \frac{mass}{volume}
• ρ = \frac{m}{V}

Pressure

• Pressure is the force divided by the area perpendicular to the force over which the force is applied.
• The formula for pressure is: P = \frac{F}{A}

Pressure and Depth

• The relationship between pressure and depth is important.
• P = \frac{F}{A} = \frac{mg}{A}
• Weight (W) = mg
• Volume = Area x height
• V = Ah
• P = \frac{mg}{A} = \frac{ρVg}{A} = \frac{ρAhg}{A} = ρgh
• Therefore, P = ρgh

Fluid Principles

• Fluids follow three principles: Bernoulli's, Pascal's, and Archimedes'.

Pascal’s Principle

• Pressure is transferred throughout a fluid.
• The change in pressure applied to an enclosed fluid is transmitted undiminished to all portions of the fluid and to the walls of its container.
• Total pressure in a fluid is the sum of the pressures from different sources.
• P1 = P2
• \frac{F1}{A1} = \frac{F2}{A2}

Buoyant Forces

• In order to float, the upward force needs to be larger than or equal to the downward force.
• Buoyant force: the net upward force of an object in any fluid.
• This force is present whether the object sinks or floats.

Archimedes' Principle

• The buoyant force on an object equals the weight of the fluid it displaces.
• Buoyant force = Weight of displaced fluid
• FB = F{g,fl}