Need a formula

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I'm trying to find Q for chimney/stove that looks very similar to the picture attached. I was going to use the formula below, but I realized that it does not account for the venturi effect if a chimney was conical in shape - i.e. smaller at the top vs. the base. Nor does it account for differences in the sizes of the air inlet and outlet.

Q=CA(sq root(2gH(Ti-To)/Ti))

[url removed, login to view]


Q = flue-gas flow-rate, m³/s

A = cross-sectional area of chimney, m² (assuming it has a constant cross-section)

C = discharge coefficient (usually taken to be 0.65–[url removed, login to view])

g = gravitational acceleration at sea level, [url removed, login to view] m/s²

H = height of chimney, m

Ti = absolute average temperature of the flue gas in the stack, K

To = absolute outside air temperature, K

I would like to know if there is a formula to find Q that would allow me to account for the following variables:

- area of the bottom air inlet

- area of the top outlet

- temp inside the chimney

- temp outside the chimney

- height of the chimney

Thanks you.

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