18.4
Moment linéaire dans le volume de contrôle
La deuxième loi de Newton est appliquée pour obtenir le moment linéaire dans un volume de contrôle dans un système fluide. Selon cette loi, le taux de…
La deuxième loi de Newton pour un système fluide stipule que le taux de variation de la quantité de mouvement linéaire dans un écoulement par rapport au temps est égal à la somme des forces externes subies par le système.
À tout instant, lorsqu'un volume de contrôle coïncide avec le système de fluides, les forces agissant sur le système et celles agissant sur le contenu du volume de contrôle sont instantanément identiques.
Lorsqu’il est appliqué au système et au volume de contrôle qui coïncide, le théorème de transport de Reynolds donne des informations importantes.
Le taux de variation temporel de la quantité de mouvement linéaire d'un système est représenté par la somme de deux composantes du volume de contrôle : le taux de variation temporel de la quantité de mouvement linéaire dans le volume de contrôle et le taux net de quantité de mouvement linéaire circulant sur la surface de contrôle.
Lorsque les particules de masse entrent ou sortent d’un volume de contrôle par la surface de contrôle, elles transportent avec elles une quantité de mouvement linéaire. Cela signifie que l’écoulement de la quantité de mouvement linéaire est tout aussi naturel que l’écoulement de la masse.
Enfin, pour un volume de contrôle fixe et non déformant, la deuxième loi de Newton peut être représentée de manière appropriée.
View the full transcript and gain access to JoVE Core videos
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.