## Related questions with answers

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.

Solutions

VerifiedFrom 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

The flowrate, $Q$, is a function of the density of the ambient air, $\rho_a$, the density of the gas, $\rho_g$, the acceleration of gravity, $g$, the height of the stack, $h$, and the diameter of the stack, $d$.

$\begin{aligned} Q&=f(\rho_a, \rho_g, g, h, d) \end{aligned}$

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