Expand divergence of velocity ∇.\(\vec{V}\) for a one-dimensional flow.(a) \(\frac{\partial u}{\partial x}+\frac{\partial v}{\partial y}+\frac{\partial w}{\partial z}\)(b) \(\frac{\partial u}{\partial x}\)(c) \(\frac{du}{dx}+\frac{dv}{dy}+\frac{dw}{dz}\)(d) \(\frac{D\vec{V}}{Dt}\)This question was posed to me at a job interview.My query is from Governing Equations topic in division Governing Equations of Fluid Dynamics of Computational Fluid Dynamics

Expand divergence of velocity ∇.\(\vec{V}\) for a one-dimensional fl

1.	Expand divergence of velocity ∇.\(\vec{V}\) for a one-dimensional flow.(a) \(\frac{\partial u}{\partial x}+\frac{\partial v}{\partial y}+\frac{\partial w}{\partial z}\)(b) \(\frac{\partial u}{\partial x}\)(c) \(\frac{du}{dx}+\frac{dv}{dy}+\frac{dw}{dz}\)(d) \(\frac{D\vec{V}}{Dt}\)This question was posed to me at a job interview.My query is from Governing Equations topic in division Governing Equations of Fluid Dynamics of Computational Fluid Dynamics
Answer» The correct option is (b) \(\frac{\partial u}{\partial X}\) Explanation: Here, \(\frac{\partial}{\partial x}\VEC{i}+\frac{\partial}{\partial y}\vec{j}+\frac{\partial}{\partial z}\vec{K}\) \(\vec{V}= u\vec{i} +v\vec{j}+W\vec{k}\) ∇.\(\vec{V}=\frac{\partial u}{\partial x}+\frac{\partial v}{\partial y}+\frac{\partial w}{\partial z}\) For one-dimensional flow, ∇.\(\vec{V}=\frac{\partial u}{\partial x}\).

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