How does the mathematical definition of drag reduce to Stokes or form drag? I know that for the flow of flow of a Navier-Stokes fluid in a domain, once the velocity $\mathbf{v}$ and pressure p are known, the drag over a solid object with boundary $\partial R$ is given by taking the component along the flow of the integral
$$ Drag = \int_{\partial R} (-p\hat{n} + \mu (\nabla \mathbf{v} + \nabla \mathbf{v}^T)\hat{n} ) da$$
However, I also read that for creeping or slow flow,
$$Drag = -b\mathbf{v}$$ This can be derived for drag on a sphere from the general formula. 
Hwever, the form drag is
$$Drag = 0.5 \; \rho\; A \; C_D ||\mathbf{v}||^2$$
Is it possible to show that the general mathematical equation for the drag reduces to the square of the velocity as stated above ?
EDIT: Thanks for pointing out the missing factor of area. Corrected now.
 A: short version: No, there is no way to show that the general integral equation for the drag reduces directly to the square of the velocity because for different flow regimes, different velocity and pressure distributions exist. 
long version: The quadratic drag equation is actually given by:
$$F_d=C_d\frac{1}{2}\rho||\mathbf{v}||^2A$$
where $A$ is usually the orthographic projected area (so a circle in case of a sphere, a square in case of a cube, etc.). This equation can be viewed as a dimensional analysis relating the drag force to the dynamic pressure ($0.5\rho||\mathbf{v}||^2$) and the area $A$ (since $p=\frac{F}{A}$) and to allow the relation to function in a wide range of flow regimes (from laminar to turbulent), a drag coefficient $C_d$ is introduced. Note: that the form may also be loosely derived from a momentum balance as suggested in the comments.
The drag coefficient in the creeping flow regime ($Re=\frac{\rho vD}{\mu}<<1$) has an analytical solution following from Stokes' drag ($F_d=6\pi\mu Rv$),
$$C_d=\frac{F_d}{\frac{1}{2}\rho v^2A}=\frac{6\pi\mu Rv}{\frac{1}{2}\rho v^2\pi R^2}=\frac{12}{Re}$$
In the turbulent regime,  there are no known solution and the value of the drag coefficient is determined experimentally or numerically. It is found to be independent of the Reynolds number with a limiting value of $O(1)$.
The use of the quadratic drag equation with the drag coefficient is the engineering approach to tying together the drag force across different regimes. It is apparently preferred to have a single relation describing the drag while the drag coefficient changes with the regimes rather than have different relations for each regime.
