(Solved):   Consider a steady, two-dimensional flow in the \( x-y \) plane whose velocity field is giv ...

 

Consider a steady, two-dimensional flow in the \( x-y \) plane whose velocity field is given by the following relation: \[ \bar{V}=(0.5+1.2 x) \vec{i}+(-2-1.2 y) \vec{j} \] (a) Obtain the location of the stagnation point in the flow field. \( (x, y)=(-0.417,-1.67) \) (b) Show that the flow satisfies the continuity equation. (5 Marks) (c) Obtain the equations for the total acceleration components. (4 Marks) \[ \begin{array}{l} a_{x}=0.6+1.44 x \\ a_{y}=2.4+1.44 y \end{array} \] (6 Marks) (Total 15 Marks) Information provided: \[ \begin{array}{l} a_{x}=\frac{\partial u}{\partial t}+u \frac{\partial u}{\partial x}+v \frac{\partial u}{\partial y}+w \frac{\partial u}{\partial z}, a_{y}=\frac{\partial v}{\partial t}+u \frac{\partial v}{\partial x}+v \frac{\partial v}{\partial y}+w \frac{\partial v}{\partial z} \\ a_{z}=\frac{\partial w}{\partial t}+u \frac{\partial w}{\partial x}+v \frac{\partial w}{\partial y}+w \frac{\partial w}{\partial z} \end{array} \]