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The fixed velocity distribution in the fully developed region is called fully developed velocity profile. The steady-state continuity and conservation of momentum equations in two-dimensional are

+ {\frac{\partial v}{\partial y}}=0 , |}}

- { { \frac{1}{\varrho}}{\frac{\partial P}{\partial x}}} + \nu \left({\frac{\partial^2 u}{\partial x^2}}+{\frac{\partial^2 u}{\partial y^2}}\right), |}}

- { { \frac{1}{\varrho}}{\frac{\partial P}{\partial y}}} + \nu \left({\frac{\partial^2 v}{\partial x^2}}+{\frac{\partial^2 v}{\partial y^2}}\right), |}}These equations can be simplified by using scale analysis. At any point in the fully developed zone, we have and . Now, from equation , the transverse velocity component in the fully developed region is simplified using scaling as |}}In the fully developed region , so that the scale of the transverse velocity is negligible from equation . Therefore in fully developed flow, the continuity equation requires that

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