Fluid Mechanics #8 - Drag and Lift of an Airfoil (Part 1): Mass Conservation and Wake Deficit

In this new video of the "Integral Theorems" series, we tackle a classic fluid mechanics application: calculating the drag and lift forces on an aerodynamic profile. We focus here on the first key step of the problem: Question 2. Using the first integral theorem, we establish the conservation of volume flow rate around the airfoil. In this video: The reference control volume (ABCDEGHIJKA). The role of the wake and the concept of flow rate deficit. Setting up the mass balance equation. Demonstrating the relationship between the integral of the velocity deficit u(x,y) and the integral of the transverse velocities v(x,y). This fundamental relationship will serve as the basis for calculating the drag in the subsequent steps. In this session, after defining the reference volume and the velocity field notations (Vx = U0 + u and Vy = v), we directly address Question 2 of the problem: mass conservation. We demonstrate that the flow rate deficit in the wake (represented by the integral of the longitudinal perturbation u) is equal to an integral of the transverse perturbation v(x,y) along the lateral boundaries of the control volume. This result is fundamental for deriving the expression of the drag force in later stages of the analysis. Useful Links: Previous Session (Session 7):    • Fluid Mechanics #7 - The Angular Momentum ...   Watch the Full Playlist on "Incompressible Fluid Mechanics" here:    • 5. Incompressible Fluid Mechanics   Watch the Full Playlist on "Perfect Fluid Mechanics" here:    • 1. Mécanique des Fluides Parfaits   Keywords: Fluid Mechanics, Integral Theorems, Drag, Lift, Airfoil, Aerodynamic Profile, Wake, Mass Conservation, Flow Rate Deficit, Control Volume, Incompressible Flow. Hashtags: #FluidMechanics #Aerodynamics #IntegralTheorems #DragAndLift #Airfoil