Question

▽(V·V)等不等于(V·▽)V? V是速度向量

Answer 1

V=ui+vj+wk

VV=u^2+v^2+w^2 (i,j,k 自乘积为1,两两乘积为0,因为它们夹角90度)

▽VV=dVV/dx+dVV/dy+dVV/dz

=[(dVV)/(dV)]*(dV/dx)+[(dVV)/(dV)]*(dV/dy)+[(dVV)/(dV)]*(dV/dz)

=[2V*(dV/dx)]+[2V*(dV/dy)]+[2V*(dV/dz)]

=2V[dV/dx+dV/dy+dV/dz]

=2V▽V