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

• pmoon.pt
In summary, there is a way to account for the venturi effect and differences in air inlet and outlet sizes when calculating the flue-gas flow rate in a chimney or stove. By using the Bernoulli's equation and the ideal gas law, you can incorporate variables such as temperature and height to get a more accurate calculation.
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

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!

## 1. What is the stack effect?

The stack effect, also known as the chimney effect, is a natural phenomenon that occurs when warm air rises and escapes out of a building through openings at the top, while cooler air is drawn in through openings at the bottom to replace it. This creates a continuous flow of air, similar to how a chimney draws smoke upwards.

## 2. What is the venturi effect?

The venturi effect is the reduction in fluid pressure that occurs when a fluid flows through a constricted section of a pipe. This reduction in pressure can create a suction force, drawing in surrounding air or fluid.

## 3. How do the stack effect and venturi effect relate to each other?

The stack effect and venturi effect are both related to the movement of air. In the case of the stack effect, warm air rises and escapes through openings at the top, while in the venturi effect, air is drawn in through a constricted area due to a decrease in pressure. In a building, these effects can work together to create a continuous flow of air.

## 4. Why would you need a formula that combines the stack effect and venturi effect?

A formula that combines the stack effect and venturi effect can be useful for calculating the amount of air flow in a building. This can be important for HVAC systems, to ensure proper ventilation and air quality, as well as for energy efficiency and cost savings.

## 5. How can I use the combined formula to find Q?

The combined formula, known as the stack-venturi formula, is used to calculate the volumetric flow rate (Q) of air in a building. It takes into account factors such as the height and temperature difference of the building, as well as the size and location of openings. By plugging in these variables, you can calculate the amount of air flow in a building, which can be useful for various purposes such as designing ventilation systems or evaluating energy efficiency.

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