literature review RANS derivation and analysis

`rho((delu)/(delt)+u(delu)/(delx)+v(delu)/(dely))=-(delp)/(rho*delx)+nu(deldel^2u)/(dely^2)`

```((delu)/(delt)+u(delu)/(delx)+v(delu)/(dely))=-(1)/(rho)(delp)/(delx)+nu(del^2u)/(dely^2).......(1.1)`

where,

`nu=(mu)/rho`

for further simplification eq^n 1.1 we add velocity is multiplied with the continuity equation i,

`u((delu)/(delx)+(delv)/(dely))`

`((delu)/(delt)+u(delu)/(delx)+v(delu)/(dely))+u((delu)/(delx)+(delv)/(dely))=-(1)/(rho)(delp)/(delx)+nu(del^2u)/(dely^2)`

`(delu)/(delt)+(delu^2)/(delx)+(delu*v)/(dely)=-(1)/(rho)(delp)/(delx)+nu(del^2u)/(dely^2)`

`(1)/(t)int(del(baru+u'))/(delt)dt+(del(baru+u')^2)/(delx)dt+(del(baru+u')(barv+v'))/(dely)=-(1)/(t)int(del(barp+p'))/(rho*(delx))dt+nu(del^2(baru+u')(barv+v'))/(dely^2)dt`.........(1.2)

wkt,

on integrating fluctuating velocity u' will be equal to zero i,e u'=0 than we get eq^n 1.3 as shown below

`(delbaru)/(delt)+(delbaru^2)/(delx)+(delbaru*barv)/(dely)=-(1)/(rho)(delbarp)/(delx)+nu(del^2baru)/(dely^2)-(1)/(t)int(del(u')^2)/(delx)dt-(1)/(t)int(del(u'*v'))/(dely)dt`................(1.3)

Note:

`int(del(u')^2)/(dely)dtne0`

`int(del(u'*v'))/(dely)dtne0`