## Drag Force Inside Boundary Layer?

I'm trying to find the total drag force on a plate that is normal to the flow of air (like a shield). And this plate is inside the boundary layer because there is another plate below (like an L shape).
I know that F_d = 1/2*Cd*density*area*velocity^2, but I have two problems...
(1) velocity is a function of y inside the boundary layer
(2) the plate is NOT a rectangle but a weirdly shaped thing that can be characterized by a function of y, such as A=A(y)

In this case, I imagine I would need to integrate to find the total drag since we have functions, but what do I exactly integrate??
My initial guess is: derive the F_d equation above and use the product rule since v=v(y) and A=A(y), and then integrate this two-term integrand. But I'm not 100% sure.

Thank you!

Context for this question: I'm trying to develop and airbrake system for a rocket, so I need to calculate the drag force these brakes will provide. Yes, I understand that using ANSYS FLUENT would be better, but I just want a rough hand-calculation as well.