Need a formula

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Project Description:
Hi,

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))
http://en.wikipedia.org/wiki/Flue_gas_stack

where:
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 0.65–0.70)
g = gravitational acceleration at sea level, 9.807 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.

Skills required:
Engineering, Mathematics, Physics
Additional Files: flow.pdf flow.jpg
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