Mr asked in Science & MathematicsEngineering · 1 month ago

Continuity of mass flow ?

State and explain the Continuity of mass flow equations for fluid which is

1) Compressible

2) incompressible

1 Answer

  • 1 month ago
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    The continuity equation is simply a statement of conservation of mass - the mass flow exiting a volume must equal the flow into the volume plus whatever mass is held in the volume from mass entering, assuming no sources or sinks of mass flow in the volume (i.e. mass either remains in the volume or leaves in the out flow).  THis is summed upped in the PDE

    dp/dt + Grad*(pU) = 0 where t = time, Grad = gradient operator, p = mass density, U = flow velocity (vector)

    In coordinates this looks like

    dp/dt + d(pU_x)/dx + d(pU_y)/dy + d(pU_z)/dx = 0

    where d/dt, d/dx, d/dy and d/dz are partial derivatives

    the first term allows for the density to change as a function of time at any point in the flow.  The second term accounts for changes in speed and density at any given time across the volume filled by the flow.

    Since this equation allows for p = p(t, x, y, z) it is valid for a compressible fluid.  If the fluid is incompressible, p = p0 = constant and then the equation becomes

    Grad*U = 0

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