question_answer

If the governing equation for a flow field is given by \[{{\nabla }^{2}}\phi \,=\,0\] and the velocity is given by \[\overrightarrow{V}\,=\,\nabla \phi ,\] the:

A) \[\nabla \times \overrightarrow{\nabla }=0\]                      

B) \[\nabla \times \overrightarrow{V}=1\]

C) \[{{\nabla }^{2}}\times \overrightarrow{\nabla }=1\]                  

D) \[(\overrightarrow{\nabla }.\nabla )\,\overrightarrow{\nabla }=\frac{\partial \,\overrightarrow{\nabla }}{\partial \,t}\]