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Reynold's Theory | Prandtl mixing length Theory

                                         Reynold's Theory Fig: Transfer of momentum in turbulent flow Relative velocity of layer 'A' w.r.t. layer 'B' is So, fluctuating components in X and Y directions due to turbulence are Vx and Vy . Now if over a surface of area 'A' perpendicular to the Y-direction and separating two adjacent fluid layers the component 'Vy ' is uniformly distributed.  So, Mass of fluid transferred across that surface from one layer to another per second =                                                        pAVy This mass of fluid has started moving with a relative velocity 'Vx'. So, Transfer of momentum = pAVxVy takes place, resulting in developing tangential forces on each of the layers. Now, the corresponding turbulent shear stress exerted on fluid layers (  𝜏 )  = pVx Vy  Since, Vx and Vy are varying, the magnitude of ' 𝜏'  will also vary. Hence, usually the time average value of  shear stress is considered