Given A liquid flows through an orifice located in the side of a tank, as shown in Fig. E$1\mathrm{.}1.$ A commonly used equation for determining the volume rate of flow, $Q,$ through the orifice is

$Q=0\mathrm{.}61A\sqrt[\phantom{2}]{2gh}$

where $A$ is the area of the orifice, $g$ is the acceleration of gravity, and $h$ is the height of the liquid above the orifice.

Find Investigate the dimensional homogeneity of this formula.

Solution The dimensions of the various terms in the equation are $Q=$ volume $\frac{?}{?}$ time $L^3{T}^{-1},A=$ area $L^2,g=$ acceleration of gravity $L{T}^{-2},$ and $h=$ height $L.$

These terms, when substituted into the equation, yield the dimensional form:

Q$=0\mathrm{.}6$Asqrt $2$gh $.$ A is area and rest is velocity $.$ Please explain fron where this eq Came