Help:lift and drag

Yap Wen Jiun

For a viscous incompressible flow past an airfoil, using the x-momentum equation and a suitable control volume the drag and lift can be calculated using the the law that the force acted on the airfoil by the control volume equal to the force acted on the control volume by the airfoil. Then taking the conservation of momentum of either the x- and y-direction, the drag which is the force in x-direction (the inlet velocity is in x-direction) can be formulated as D=Sum (pressure force + density * velocity^2) at inlet - sum (pressure force + density * velocity^2) at outlet and lift, L is formulated with the almost same formulation. As this formula is directly derived from the Navier-Stoke equation for viscous, newtonian flow, it should be valid (a little error tolerance) for whatever control volume should be as long as the airfoil is surrounded by the control volume. Am I right ? But I found different answer using this formula for both the drag and lift for different control volume in PHOENICS. Is this formula a very cruel approximation ? What is its limitation ? If so, why is this formula can be found in almost all the books for aerodynamics?

I can give more details about how I use this formula (in PHOENICS) if needed. So please help me.