The Chezy$-$Manning equation below provides a formula for calculating average velocity U of flow through an open channel in terms of the hydraulic radius R$\_($h$)$ of the channel, bottom bed slope of the channel, S$\_(0)($where S$\_(0)$ can be defined as change in water depth over a given channel length$)$ and dimensionless roughness coefficient of the channel n$.$ What are the dimensions of $\backslash$kappa