Fluid Mechanics Newtons law of viscosity

[wozzers]

Homework Statement

having problems differentiating

Homework Equations

Tw ( wall shear stress)= -U(viscosity)*du/dr
been given u as 2V(1-(r/r)^2)

The Attempt at a Solution

i substituted u in and got

d/dr (2V(1-(r/r)^2)
i tried to multiply out the minus sign and 2V and got a very different answer i got -2V+2V (r/r)^2

when the answer is supposed to be -4VR/R^2

please help

 

[janhaa]

What do you mean here:

been given u as
2V(1-(r/r)^2) = 2V(1 - 1) = 0

?

 

[pasmith]

Homework Statement

having problems differentiating

Homework Equations

Tw ( wall shear stress)= -U(viscosity)*du/dr
been given u as 2V(1-(r/r)^2)

Do you mean
<br /> u = 2V\left(1 - \left(\frac{r}{r_0}\right)^2\right)<br />
where r_0 is the radius of what I assume to be a cylindrical pipe?

The Attempt at a Solution

i substituted u in and got

d/dr (2V(1-(r/r)^2)
i tried to multiply out the minus sign and 2V and got a very different answer i got -2V+2V (r/r)^2

when the answer is supposed to be -4VR/R^2

please help

The given answer is for du/dr; to get T_w you have to multiply that by -\mu.

So far all you've done is multiply u by -1. Try differentiating with respect to r first.

 

[wozzers]

r=R and its (r/R)^2

 

[wozzers]

okay now i have differentiated it with respect to r i get 2V2r/R^2) or -(4Vr/R^2) thanks again i was then required to use the wall shear stress to determine the frictional force but it is very straight forward from there