[4asino]

if r=f(x,z) as r:radius & x:x distance & z: z distance
a=f(u,w) as a:axial velocity & u:x velocity component & w:z velocity component
I want to get (da/dr) as I have only the values of
du/dx & du/dz & dw/dx & dw/dz

[FMDenaro]

Originally Posted by 4asino

if r=f(x,z) as r:radius & x:x distance & z: z distance
a=f(u,w) as a:axial velocity & u:x velocity component & w:z velocity component
I want to get (da/dr) as I have only the values of
du/dx & du/dz & dw/dx & dw/dz

sorry but your question is not very clear to me ....

u and v are funcion of (x,z) only? the function f is the same ???

[4asino]

r is curvature radius in xz plane , so r is a function of x,z
a is axial velocity in curvature axis dimension , and so it is a function of u (x-velocity component ) and w (z-velocity component )

I want a direct relation between variation of axial velocity through r-direction.

In cfd i can get du/dx , du/dz, dw/dx, dw/dz only

and so i want da/dr using only the four differentials

[FMDenaro]

Originally Posted by 4asino

r is curvature radius in xz plane , so r is a function of x,z
a is axial velocity in curvature axis dimension , and so it is a function of u (x-velocity component ) and w (z-velocity component )

I want a direct relation between variation of axial velocity through r-direction.

In cfd i can get du/dx , du/dz, dw/dx, dw/dz only

and so i want da/dr using only the four differentials

r=r(x,z) and a=a[u(x,z),w(x,z)]

Therefore you can get the total differential da = da/du du + da/dw dw and then developping further

[4asino]

r=(x^2+z^2(^0.5
a^2=(u^2+w^2)

da/du=u/a
da/dw=w/a

da=da/du *du +da/dw *dw
=u/a *du + w/a *dw

what is the value of du or dw ? Are they equal to (du/dx or du/dz) or (dw/dx or dw/dz) ?

[FMDenaro]

Originally Posted by 4asino

r=(x^2+z^2(^0.5
a^2=(u^2+w^2)

da/du=u/a
da/dw=w/a

da=da/du *du +da/dw *dw
=u/a *du + w/a *dw

what is the value of du or dw ? Are they equal to (du/dx or du/dz) or (dw/dx or dw/dz) ?

no, I defined the total differential as function, therefore you have to consider

du = du/dx dx + du/dy dy

and similar for dw

[4asino]

That's good & all thanks
also, I should have values of dx & dz ! Is this right ?
How can I get their values ? i.e from a certain point (0,0) or assumption ?

[FMDenaro]

they are the incremental of the position x,z starting from x0,y0 as you do in a Taylor expansion