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~viscous~

!force convention.jpg!


Drag due to pressure:
\\
{latex}
\large
$$
{(Drag)_{pressure}} = {\oint \-P \hat{n}.\hat{e_d}dS}
$$
{latex}

\\
{latex}
\large
$$
{(Drag)_{viscous}} = {\oint \tau_w \hat{t}.\hat{e_d}dS}
$$
{latex}
where

_e{_}{_}{~}d{~}_ is the unit vector parallel to the flow direction. 

_n_ is unit vector perpendicular to the surface of airfoil.

_t_ is unit vector parallel to the surface of airfoil.
\\

Similarly, if  we are interested in the lift on the airfoil,

(Lift) = (Lift)~pressure~ + (Lift)~viscous~

Lift due to pressure:
{latex}
\large
$$
{(Lift)_{pressure}} = {\oint \-P \hat{n}.\hat{e_l}dS}
$$
{latex}

\\
{latex}
\large
$$
{(Lift)_{viscous}} = {\oint \tau_w \hat{t}.\hat{e_l}dS}
$$
{latex}
where

_e{_}{_}{~}l{~}_ is the unit vector perpendicular to the flow direction. 

_n_ is unit vector perpendicular to the surface of airfoil.

_t_ is unit vector parallel to the surface of airfoil.
\\