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# Assume that the flowrate. Q, of a gas from a smokestack is a function of the density of the ambient air,$\rho_{a}$, the density of the gas,$\rho_{g}$, within the stack, the acceleration of gravity, g, and the height and diameter of the stack, h and d, respectively. Use $\rho_{c}$, d, and g as repeating variables to develop a set of pi terms that could be used to describe this problem.

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From the statement of the problem we can write the functional equation as following to list all the variables that are involved in the problem:

{\color{#4257b2}\begin{align*} Q = f(\rho_{a},\ \rho_{g},\ g,\ h,\ d) \end{align*}}

Where this equation expresses the general functional relationship between the flowrate $(Q)$, and the several variables that will affect it such as the density of the ambient air $(\rho_{a})$, the density of the gas$(\rho_{g})$, within the stack, the acceleration of gravity (g), and the height and diameter of the stack (h) and (d), respectively

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