Linear momentum equation for steady flow with fixed control volume is given by [Where, V : Velocity vector, \(\hat n\): outward normal unit vector of area dA, F = forces on control volume]:
1
\(\sum F = \mathop \smallint \nolimits_{cs} \rho V(V.\hat n)\;dA\)
2
\(\sum F = \mathop \smallint \nolimits_{cs} \rho V(V \times \hat n)dA\)
3
\(\sum F = \mathop \smallint \nolimits_{cs} \rho \left( {V \times V} \right) \cdot \hat ndA\)
4
\(\sum F = \mathop \smallint \nolimits_{cs} \rho (V \cdot \hat n)dA\)