Just as see in pics. Conservation of Mass: u/ x + v/ y = 0 In the context of flo

Question

Just as see in pics.

Conservation of Mass: u/ x + v/ y = 0 In the context of flow through a differential control volume, what is the physical significance of the foregoing terms, if each is multiplied by the mass density of the fluid? Newton's Second Law of Motion: x-direction: u u/ x + v u/ y = - 1/rho dp infinity/dx + v 2u/ y2 What is the physical significance of each term in the foregoing equation? Why can we express the pressure gradient as dp infinity/dx instead of p / x? Conservation of Energy: u T/ x + v T/ y = alpha 2T/ y2 + v/cp( u/ y)2 What is the physical significance of each term in the foregoing equation? What is the second term on the right-hand side called and under what conditions may it be neglected?

Explanation / Answer

conservation of mass

if each term is multiplied by mass density,this equation will be called steady two dimensional flow of a compressible fluid.

newton second law of motion

physical significance

*the term in left hand side represent net outflow of momentum in x direction

*the first term on right hand side i.e. -1/p*d(p)/d(x) represent force because of variation of pressure in x- direction.

*the last term on right hand side represents net viscous force.

*when gravity effects and other body forces are negligible and the boundary layer approximation are valid,applying newton's second law in on volume element in y direction gives the y- momentum equation

partial(P)/partial(Y)=0

that is variation of pressure in the direction noremal to the surface is negligible and thus P=P#

and partia l(P)/partial(Y)= d(P)/d(X)

*conservation of energy

the term on left hand side represnt net energy convected by fluid out of control volume

and first term on right hand side represent net enrgy transfered into control volume by heat conduction

second term on right hand side represnt energy dissipated due to shear stress

second term on right hand sideis called viscous dissipation function

and it is neglected when there is low speed fluid flow and viscosity is low.

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