Shear stress in directions other than the flow direction

Shear stress in directions other than the flow direction

I already asked this question here
http://physics.stackexchange.com/questions/74310/shear-stress-in-directions-other-than-the-flow-direction,
but Ii am not getting a response. I think applied mathematicians should be
able to answer the question.Thus, I don't think the question is off-topic.
Consider the flow of a newtonian fluid in a rectangular pipe. Consider a
3D coordinate system with the property that.that the flow of the fluid in
the pipe is parallel to the x-axis. Let $V:\mathbb{R}^3\rightarrow
\mathbb{R}^3$ return the velocity vector at each point of the 3D space.
Assume that $V$ is differentiable with continuous partial derivatives.
Consider a cuboid inside the fluid filling the pipe: $[x_0,x_0+\triangle
x]\times [y_0,y_0+\triangle y]\times [z_0,z_0+\triangle z]$ . I am trying
to compute the shear force on the face $\{(x_0,y,z)|y_0\leq y\leq
y_0+\triangle y,z_0\leq z\leq z_0+\triangle z\}$ of the cuboid. My guess
that it would be:
$$\int_{y_0}^{y_0+\triangle y}\int_{z_0}^{z_0+\triangle z}
\mu[v_x(x_0,b,c)+v_z(x_0,b,c)]dc
\,db\,\mathbf{j}+\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\int_{y_0}^{y_0+\triangle
y}\int_{z_0}^{z_0+\triangle z} \mu[w_x(x_0,b,c)+w_y(x_0,b,c)]dc
\,db\,\mathbf{k}$$ (Note about the notation:
$V(x,y,z)=u(x,y,z)\mathbf{i}+v(x,y,z)\mathbf{j}+w(x,y,z)\mathbf{k}$)
Am I right? If I am not right could you please give the correct shear
force on the face I am talking about.
Sorry if the question is naive. If the question is naive it would probably
be because I only had an engineering course in fluid mechanics and the
course considered only shear stress parallel to the direction of flow. I
don't know if this is because shear stress only acts in the direction of
shear flow or because the book was assuming (without mentioning) that some
components of $V$ are zero or have zero partial derivatives. Thus the only
equation for shear stress I saw in the course is $\tau=\mu \frac{\partial
v}{\partial y}$. I am looking for the most general case.
Thank you