18.4
Momento lineal en el volumen de control
La segunda ley de Newton se aplica para obtener el momento lineal en un volumen de control en un sistema de fluidos. Según esta ley, la tasa de cambio…
La segunda ley de Newton para un sistema de fluidos establece que la tasa de cambio del momento lineal en un flujo con respecto al tiempo es igual a la suma de las fuerzas externas que experimenta el sistema.
En un instante dado, cuando un volumen de control coincide con el sistema de fluidos, las fuerzas que actúan sobre el sistema y las que actúan sobre el contenido del volumen de control son instantáneamente idénticas.
Cuando se aplica al sistema y al volumen de control coincidente, el teorema de transporte de Reynolds proporciona información importante.
La tasa de cambio de tiempo del momento lineal de un sistema se representa como la suma de dos componentes del volumen de control: la tasa de cambio de tiempo del momento lineal dentro del volumen de control y la tasa neta de momento lineal que fluye a través de la superficie de control.
A medida que las partículas de masa entran o salen de un volumen de control a través de la superficie de control, llevan consigo un momento lineal. Esto significa que el flujo de momento lineal es tan natural como el flujo de masa.
Por último, para un volumen de control que es fijo y no deformante, la segunda ley de Newton se puede representar adecuadamente.
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Q1: How does Newton's second law apply to fluid flow in a control volume?
Newton's second law for a fluid system states that the rate of change of linear momentum equals the sum of external forces acting on the system. When a control volume coincides with the fluid system at any instant, the forces on both are identical. This principle forms the foundation for analyzing momentum changes in fluid dynamics and enables engineers to predict system behavior under various flow conditions.
Q2: What does the Reynolds transport theorem reveal about momentum in a control volume?
The Reynolds transport theorem breaks down a system's linear momentum into two components: the time rate of change of momentum within the control volume and the net rate of momentum flowing across the control surface. This decomposition allows engineers to separately account for internal momentum changes and momentum transport due to mass entering or leaving the control volume boundaries.
Q3: How does mass movement affect momentum transfer across a control surface?
As particles of mass enter or exit a control volume through the control surface, they carry linear momentum with them. The flow of linear momentum is as natural as the flow of mass itself. This momentum transfer is a key consideration when analyzing forces and motion in fluid systems, making it essential for solving real-world engineering problems involving flowing fluids.
Q4: Why is it important to distinguish between momentum inside and outside a control volume?
Distinguishing between internal momentum changes and momentum crossing the control surface allows engineers to apply Newton's second law accurately to fixed regions of flow. This separation enables precise force calculations and helps predict how external forces influence fluid motion. Understanding both components is critical for designing systems like pumps, turbines, and channels where momentum management is essential.
Q5: What conditions must a control volume meet for Newton's second law to apply accurately?
For a control volume that is fixed and nondeforming, Newton's second law can be suitably represented to analyze system dynamics. Fixed, nondeforming control volumes provide a stable reference frame for tracking momentum changes and external forces. This configuration is ideal for most engineering applications, including pipe flow analysis and channel design where the control volume boundaries remain stationary and rigid.
Q6: How do external forces relate to momentum changes in a control volume?
External forces acting on a control volume directly determine the rate of change of linear momentum within it. The sum of all external forces equals the total momentum change, accounting for both internal momentum variations and momentum transport across boundaries. This relationship is fundamental to the application of the linear momentum equation in solving engineering problems involving fluid flow and force analysis.
Q7: Why is the control volume approach essential for analyzing fluid systems?
The control volume approach provides a systematic framework for analyzing forces, motion, and interactions within well-defined regions of flow. By applying Newton's second law to a control volume, engineers can account for momentum changes due to both internal fluid dynamics and mass transport across boundaries. This method is applicable to a wide range of engineering problems, from hydraulic structures to industrial fluid systems.