Fluid Mechanics #6 - Variants of the use of the Momentum Theorem

Hello everyone and welcome to this sixth session of our Fluid Mechanics course. After applying the Momentum Theorem to external flows in the previous video, we will now dive deep into the variants of its use. These subtleties are crucial for correctly understanding what we are calculating and for avoiding common mistakes. In this session, we will cover: 1. Absolute or Relative Pressure? (Question 1) We address a frequently asked question: when using pressure p in the Momentum Theorem, does it represent absolute or relative pressure? I will show you why, thanks to the gradient theorem, the choice of the reference pressure ultimately has no effect on the final result. It is strictly equivalent. 2. Static or Driving Pressure? (Question 2) We explore another essential variant: the difference between static pressure and driving pressure p* = p + ρgz. We will see how using driving pressure allows us to omit the weight of the fluid in the calculations and simplify the equation. Important consequence: We discuss the force Fi exerted by the fluid on the body, which includes the buoyancy force, as opposed to the force Fi* exerted solely by the flow, which does not. 3. The Momentum Flux Correction Coefficient β (Question 3) In reality, the velocity is not uniform over a cross-section (laminar or turbulent profile). How do we calculate the momentum flux then? I introduce the dimensionless coefficients β1 and β2, which correct this flux. Typical values: Uniform flow: β = 1 Turbulent flow: β ≈ 1.03 Laminar flow: β = 1.33 We will see that, to estimate the order of magnitude of a force, we can often take β = 1 Who is this for? This session is intended for undergraduate science students, preparatory class students, or engineering students who want to master the finer points of the momentum theorem in fluid mechanics. Useful Links: Previous Session (Session 5):    • Fluid Mechanics #5 - Momentum Theorem for ...   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: Momentum Theorem, Fluid Mechanics, Absolute Pressure, Relative Pressure, Static Pressure, Driving Pressure, Buoyancy Force, Archimedes' Principle, Momentum Flux Correction Coefficient, Boussinesq Coefficient, Laminar Flow, Turbulent Flow, Incompressible Flow, Control Volume, Aerodynamic Force, External Flow, Internal Flow, Gradient Theorem, Fluid Dynamics, Engineering Physics Hashtags #FluidMechanics #MomentumTheorem #ExternalFlow #Aerodynamics #ControlVolume #CutSurface #WindTunnel #AeroForce #Engineering #MechanicalEngineering #FluidDynamics