3) (25 points) As an engineer before taking velocity measurements in a smokestack at a factory, you are asked to obtain

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3) (25 points) As an engineer before taking velocitymeasurements in a smokestack at a factory, you are asked to obtainthe important dimensionless terms to describe the flow rate of theexhaust gas in terms of the dimensionless gas and airflowparameters and dimensionless geometric dimensions of thesmokestack. Using the Buckingham Pi theorem for dimensionalanalysis, develop these terms using the following variables. Usethe diameter of the smokestack, density of ai, and gravitationalacceleration as repeating variables.
Q = flow rate of the exhaust gas 𝜌𝑎= Air density𝜌𝑔 = Exhaust gas density
𝑔 = Gravitational accelerationh = Height of the smokestack𝑑 = Diameter of the smokestack