Need a formula that combines the stack effect + venturi effect to find Q

[pmoon.pt]

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 in advance!

 

[AndyW]

Hi there,

Thank you for your question. The formula you have mentioned is a good starting point for calculating the flue-gas flow rate in a chimney or stove. However, as you have pointed out, it does not account for the venturi effect or differences in the sizes of the air inlet and outlet.

To account for these variables, you can use the Bernoulli's equation, which takes into consideration the velocity of the fluid, the pressure, and the density. This equation can be applied to a conical chimney or stove, as well as different sizes of air inlets and outlets.

The equation is as follows:

Q = A1*v1 = A2*v2

Where:
Q = flue-gas flow rate, m³/s
A1 = cross-sectional area of the bottom air inlet, m²
A2 = cross-sectional area of the top outlet, m²
v1 = velocity of the flue gas at the bottom air inlet, m/s
v2 = velocity of the flue gas at the top outlet, m/s

To calculate the velocities, you can use the following equations:

v1 = sq root(2*(P1-P2)/ρ*(1-(A1/A2)^2))

v2 = sq root(2*(P1-P2)/ρ)

Where:
P1 = pressure at the bottom air inlet, Pa
P2 = pressure at the top outlet, Pa
ρ = density of the flue gas, kg/m³

To find the pressure at the bottom air inlet and top outlet, you can use the ideal gas law:

P = ρ*R*T

Where:
P = pressure, Pa
ρ = density of the flue gas, kg/m³
R = specific gas constant for the flue gas, J/kgK
T = temperature, K

By using these equations, you should be able to calculate the flue-gas flow rate with more accuracy, taking into consideration the variables you have mentioned. I hope this helps. Good luck with your research!