Fluids

What defines a fluid?

A fluid is anything that flows, including liquids, gases, and in-between states.

What is density?

Density (ρ) is the mass (m) of a substance divided by its volume (V), expressed as ρ=m/V.

How is pressure (P) defined?

Pressure is the force (F⊥) applied by a fluid over a given area (A), given by the formula P=F⊥/A.

What is Pascal’s Law?

Pascal's Law states that a change in pressure applied to an enclosed fluid is transmitted undiminished throughout the fluid.

What is the equation for absolute pressure (P) at a depth?

Absolute pressure increases with depth and is given by P=P0+ρgh, where P0 is atmospheric pressure.

What is buoyancy?

Buoyancy is the upward force exerted by a fluid, equal to the weight of the displaced fluid; if the buoyant force (Fb) is greater than the object's weight, it floats.

What is the continuity equation for fluid flow?

The continuity equation states A1v1=A2v2, meaning the volume flow rate is constant in a pipe, regardless of shape changes.

What is Bernoulli’s equation?

Bernoulli's equation relates pressure, gravitational potential energy, and kinetic energy in a fluid: P1+ρgy1+0.5ρv1²=P2+ρgy2+0.5ρv2².

What is Torricelli’s Theorem?

Torricelli's Theorem states that the speed (v) of a fluid draining from a hole is given by v=√(2gΔy), where Δy is the height difference.

What happens to fluid speed in narrowed spaces?

As a fluid moves into a narrower section, its velocity increases to maintain the same flow rate (A1v1=A2v2).