The dimension of the velocity gradient is [M0L0T−1][M^0L^0T^{-1}][M0L0T−1]. This is because the velocity gradient is the change in velocity per unit distance. Mathematically,

Velocity Gradient=ΔVΔL\text{Velocity Gradient}=\frac{\Delta V}{\Delta L}Velocity Gradient=ΔLΔV​

where velocity VVV has dimension [M0L1T−1][M^0L^1T^{-1}][M0L1T−1] and distance LLL has dimension [M0L1T0][M^0L^1T^0][M0L1T0]. Thus,

Dimension of velocity gradient=[M0L1T−1][M0L1]=[M0L0T−1]\text{Dimension of velocity gradient}=\frac{[M^0L^1T^{-1}]}{[M^0L^1]}=[M^0L^0T^{-1}]Dimension of velocity gradient=[M0L1][M0L1T−1]​=[M0L0T−1]

This means the dimension of velocity gradient is the same as that of frequency (inverse time).