Mecánica de fluidos | Ecuación de continuidad

Continuity Equation for Ideal Fluids

Characteristics of an Ideal Fluid

• An ideal fluid is characterized by being non-viscous, laminar flow, incompressible, and irrotational.

• Non-viscous means internal friction forces within the fluid are negligible.

• Laminar flow indicates that particles in the fluid follow smooth paths without crossing each other, resembling parallel sheets.

• Incompressible fluids maintain constant volume under external forces; their density does not change.

• Irrotational implies there is no rotational movement in the flow or among its constituent particles.

Analysis of Flow Volumes

• When a certain volume of water enters through a hose at one end, it must displace an equal volume out at the other end due to incompressibility.

• The volumes entering and exiting are analyzed over a distance: delta x1 for entry and delta x2 for exit.

• Each volume moves with specific velocities (v1 for entry and v2 for exit), allowing us to express distances traveled as functions of time.

Deriving Volume Expressions

• The volume of a cylinder can be calculated using the formula: Volume = Area × Height. Here, height corresponds to either delta x1 or delta x2.

• For Volume 1: V1 = Area 1 × Velocity 1 × Time; similarly for Volume 2: V2 = Area 2 × Velocity 2 × Time.

• Since both volumes are equal (V1 = V2), we can equate these expressions and cancel out time to derive a key equation.

Continuity Equation

• The resulting equation from equating volumes leads to A1 × v1 = A2 × v2, known as the continuity equation.

• This equation states that the product of area and velocity remains constant along any section of flow.