I am trying to determine the horizontal pressure gradient in a scenario where water is drained out from the bottom of a tub. The height of the water surface varies by $0.01$m over horizontal distance of $0.10$m and water speeds in the tub are $0.3$m/s.
From the equation $$\text{pressure}=\text{force}/\text{area}\implies \text{pressure}=\rho g h.$$ Here, $\rho$ is the density of water, $g$ is the acceleration due to gravity at the surface and $h$ is the height of the liquid column/depth in the substance.
Thus, \begin{align} \text{pressure}&=997 \ \text{kg/m$^3$}\cdot 9.81\ \text{m/s$^2$}\cdot 0.01 \ \text{m} \\ &=97.8057 \ \text{Pa}. \end{align} Dividing this by $0.1$m gives $978.057$ Pa/m. Is this solution valid?