in the face bcgf why have we added ddxpudydzdx in pudydz FUN

in the face bcgf why have we added d/dx(pudydz)dx in pudydz

FUNDAMENTAL OF FLUID FLOW INUITY EQUATION IN THREE DIMENSIONS e dimensional fluid element having dimensions ig. 5.15. d w be the inlet velocity components along, ions respectively. uid entering the face ADHE per second =Density x Velocity x Area ofADHE f E U dz dy luid leaving the face BCGF per second y FIG. 5.15 Three ax dimensional fluid element in mass per second by the fluid element along ax dx ·dyde is constan (pu) dxdydz Ox

Solution

Solution:

The fixed region inside the parallelopiped is the control volume . The control volume is dx dy dz.

The amount is added because the amount of fluid leaving that face is a combination of mass entering ADHE face PLUS the rate of accumulation mass in control volume in the +X direction.

This is because the change in velocity over a distance of dx in the x direction is du/dx dx.

If the fluid mass flows out of the system more quickly than the mass that flows into the system , then there will be the accumulated volume inside the parallelopiped ( control volume) .

There is also fluid flowing through the face ABFE.