In cartesian co-ordinate ($x,y,z$), gradient of velocity($\mathbf{u}=(u_x,u_y,u_z)$)(Jacobian matrix)is defined: \begin{equation*} \nabla \mathbf{u}= \begin{pmatrix} \partial_x u_x && \partial_y u_x&&\partial_z u_x \\ \partial_x u_y && \partial_y u_y&&\partial_z u_y \\ \partial_x u_z && \partial_y u_z&&\partial_z u_z \end{pmatrix} \end{equation*} Then what is the gradient of velocity ($\mathbf{u}=(u_r,u_\theta,u_z)$), in cylindrical coordinate($r,\theta,z$)? and how we derive that?


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