13.17
Ecuación de Continuidad
El movimiento de un fluido se representa mediante vectores de velocidad o líneas de corriente. El volumen de un fluido que pasa por una ubicación dete…
El volumen de fluido que fluye a través de un punto en un área en unidad de tiempo da el caudal volumétrico.
Al sustituir el volumen por el área por la distancia, y utilizando la relación entre la velocidad y la distancia, el caudal volumétrico es igual al área por la velocidad del fluido.
Considere un fluido incompresible con la misma densidad en todos los puntos que fluye constantemente a través de una tubería de sección transversal irregular. Para un flujo constante, la velocidad y la densidad del fluido en un punto permanecen constantes con el tiempo.
La masa del fluido que pasa a través de un punto por unidad de tiempo se denomina caudal másico y es igual a la densidad por el caudal volumétrico.
Dado que la tubería no tiene ninguna otra fuente o sumidero, la masa que fluye hacia la tubería debe ser igual a la masa que sale de la tubería. Esto da la ecuación general de continuidad para los fluidos.
En el caso de los fluidos incompresibles, la densidad se anula. Por lo tanto, el caudal volumétrico en la tubería es igual al caudal volumétrico fuera de la tubería.
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Q1: What is volume flow rate and how is it calculated?
Volume flow rate is the volume of fluid flowing through a point in an area per unit time. It is calculated by multiplying the cross-sectional area of the pipe by the velocity of the fluid. This relationship shows that flow rate depends on both the size of the conduit and how fast the fluid moves through it.
Q2: Why does fluid velocity increase when a pipe narrows?
When a pipe's cross-sectional area decreases, the fluid velocity must increase to maintain continuity of flow. Since the same amount of incompressible fluid must pass through any point in the pipe per unit time, a smaller area requires higher velocity to conserve the volume flow rate.
Q3: What is the equation of continuity for incompressible fluids?
The equation of continuity states that the volume flow rate entering a pipe equals the volume flow rate leaving it. For incompressible fluids, density cancels out, so the product of cross-sectional area and velocity remains constant throughout the pipe, ensuring mass conservation.
Q4: How does mass flow rate relate to volume flow rate?
Mass flow rate equals density multiplied by volume flow rate. It represents the mass of fluid passing through a point per unit time. For steady flow through a pipe with no sources or sinks, the mass flowing in must equal the mass flowing out.
Q5: What conditions must be met for steady flow in a pipe?
For steady flow, the velocity and density of the fluid at any point must remain constant over time. Additionally, the pipe must have no sources or sinks that add or remove fluid, ensuring that mass entering the pipe equals mass leaving it at all times.
Q6: Why is the equation of continuity valid for liquids but not always for gases?
Liquids are essentially incompressible, so their density remains constant, making the equation of continuity universally valid for all liquid flow. Gases are compressible, so the equation must be applied with caution when gases undergo compression or expansion, as density changes affect flow relationships significantly.
Q7: How does the equation of continuity relate to energy conservation in fluid flow?
The equation of continuity ensures mass conservation in steady flow by maintaining constant volume flow rate through varying pipe sections. This principle connects to energy conservation and bernoulli equation principles, where changes in velocity and pressure are governed by both mass continuity and energy conservation in fluid systems.