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For the flow of air exiting a pipe, the updraft velocity is a function of the thermal energy input (heat) and is described by the principles of the stack effect. In this phenomenon, heated air is less dense and creates a pressure difference that drives the flow.The updraft equation links the thermal energy, which is characterized by the temperature difference, to the resulting mass flow rate. Stack effect equation for flow rate The stack effect equation is a practical model for calculating the flow rate Q generated by a temperature differential. Q=C_{d}A\sqrt{2gH\frac{T_{i}-T_{o}}{T_{i}}}
where:
Q = flow rate typically in cubic feet per minute or m^{3}/s
C_{d} = discharge coefficient (for a smooth pipe opening, usually 0.65 to 0.70
A = cross-sectional area of the pipe m^{2}
g = gravitational acceleration 9.81\,m/s^{2}H = effective height of the pipe mT_{i} = average indoor or internal temperature (Kelvin)T_{o} = outdoor or external temperature (Kelvin)
This equation can be simplified for an enclosed pipe with a known height and a large opening.
It shows that flow rate is directly proportional to the square root of the temperature difference, T_{i}-T_{o}.
Relating thermal energy input to temperature change
The thermal energy input is related to the change in the air's internal temperature by the fundamental heat transfer equation: q=\.{m}c_{p}\Delta T where: q = rate of heat input W or J/s\.{m} = mass flow rate of air kg/sc_{p} = specific heat capacity of air at constant pressure 1005\,J/(kg\cdot K)\Delta T = change in temperature of the air as it passes through the pipe K Calculating updraft velocity To determine the velocity v of the exiting air, you can use the mass flow rate \.{m} and the air's final density \rho _{exit}: v=\frac{\.{m}}{\rho _{exit}A} where: \.{m} = mass flow rate kg/s\rho _{exit} = density of the air exiting the pipe kg/m^{3}A = cross-sectional area of the pipe m^{2}
By linking these equations, you can model how a specific thermal energy input q translates into a temperature change, which then drives the air flow Q and determines the exit velocity v.
The updraft is a self-sustaining process driven by the buoyancy created from the thermal energy input
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A "hot chimney updraft pipe" is the central component of a chimney system where an updraft, or the upward flow of hot exhaust gases, is created and maintained. This upward movement is driven by the principle that hot air is less dense than cold air, causing it to rise.
How the updraft works
The updraft is the engine of a chimney, pulling smoke and combustion gases out of a building and supplying the fire with fresh oxygen.
Temperature difference: The heat from a fire warms the air and gases inside the chimney, making them lighter than the cooler air outside. This temperature difference causes the hot, lighter air to rise.
Pressure difference: The rising hot air creates a negative pressure (low-pressure area) inside the chimney, which pulls air from the firebox and the surrounding area upward. Meanwhile, higher-pressure atmospheric air is pushed into the appliance's air intake, feeding the fire with oxygen.
Continuous cycle: This process establishes a continuous cycle of airflow that ensures smoke and dangerous carbon monoxide are vented safely outside.
Factors affecting the updraft
Several factors can influence the strength and reliability of a chimney's updraft:
Chimney height: A taller chimney generally produces a stronger updraft because it increases the pressure difference between the top and bottom of the flue. The general rule for residential systems is that the chimney pipe must be at least 3 feet above the roof and 2 feet taller than anything within 10 feet.
Temperature difference: A greater temperature difference between the inside and outside air results in a stronger draft. For example, a cold chimney can cause a reverse draft or "backdraft" when you first start a fire.
Obstructions: Blockages like soot, creosote, or debris can restrict airflow and weaken the draft.
Negative air pressure: Air-tight modern homes can create a negative pressure environment that works against the chimney's natural draft. Installing a combustion air kit or opening a window slightly can help.
Pipe configuration: Excessive bends or horizontal runs in a chimney pipe can decrease the draft, as each turn adds friction and slows the airflow.
Solving updraft issues
If a chimney isn't drafting properly, it can fill a room with smoke, which is a serious health and safety hazard. Solutions include:
Pre-heating the flue: To fix a cold backdraft, you can warm the flue with a rolled-up, lit newspaper or a heat gun for a few minutes before starting the fire. This creates a small, initial updraft to get the system working correctly.
Proper sealing: Seal any gaps or cracks around the fireplace or chimney to prevent air leaks.
Damper installation: Consider installing an air damper to better regulate airflow.
Wind considerations: A chimney cap with a special design, such as a Vacu-Stack, can prevent wind from blowing back down the chimney
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The reverse of this option is the downdraft chimney. For this idea, water is sprayed at the top of the tower, cooling the air, which is then denser than the air around it. The dense air sinks down the tower, flowing through a turbine at the bottom. The plus side it that you don't need a huge greenhouse to make this work. This might be a good option in places with hot climate. Potentially, seawater could be used rather than freshwater. In places that are arid, this would add moisture to the air and could therefore create rain. It would also create a layer of cool air close to the ground, which would reduce the need for air conditioning.
There are some states in the southern US that could benefit from this technology. The towers could be made from thin concrete shells, rather like cooling towers. In additional to generating power, the towers coukd be used to cool urban areas, either by venting cool air at the bottom of the tower creating a dense, ground hugging layer, or by piping cool air to specific buildings.
Individual houses could be cooled using small downdraft towers. This could replace other types of air conditioning and could be entirely solar powered. Alternatively, multiple houses could be clustered around a single downdraft tower, with each supplied with air via buried ducts. A well designed system could provide cool air without any expenditure of power.
Last edited by Calliban (Today 02:09:11)
"Plan and prepare for every possibility, and you will never act. It is nobler to have courage as we stumble into half the things we fear than to analyse every possible obstacle and begin nothing. Great things are achieved by embracing great dangers."
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