A commonly-used formula to estimate flow velocity, u, in an open channel is given by the equation: V - k n W A 2/3 $1/2 where the magnitude of k is 1.468, n = 0.05 is a unitless quantity representing the "roughness" of the channel, A is the cross-sectional area of the river, W is a length scale representative of the river width [NOTE: we will discuss exactly how this is computed later in the semester], and S is the slope of the river bed. The formula yields a velocity in units of meters per second when A and W are in units of meters. (a) Is the constant, k, dimensionless? If not, what are the dimensions? (b) Would this equation be valid if units other than meters and seconds were used?