Chimney diameter
Thread Content
It is already known that the diameter at the outlet of the chimney is 3 m and the height of the chimney is 70 m. Can the diameter at the bottom of the chimney be calculated? Or what other conditions are needed to determine it? Please give me some advice, thank you!
It is not possible to determine the diameter at the bottom of the chimney based on the conditions you provided. The axial cross-section of the chimney is a trapezoid, with the outlet diameter representing the upper base of the trapezoid, the bottom diameter representing the lower base, and the height of the chimney corresponding to the height of the trapezoid. Even with the upper base and height of a trapezoid, it’s not possible to determine its properties. To determine this, it is also necessary to know the angle between the trapezoid’s sides and its height, or in other words, the taper of the chimney.
The diameter D at the base of the chimney can be determined based on the top diameter d and the chimney’s taper. That is, D = d + 2αH. For reinforced concrete chimneys, the taper angle α is usually set at 0.01; for brick chimneys, D = 1.5d. Therefore, for your question, the diameter at the base of the chimney can be calculated as follows: ① D = d + 2αH = 3 + 2×0.01×70 = 4.4 (meters), or ② D = 1.5d = 1.5×3 = 4.5 (meters)
The diameter D at the base of the chimney can also be calculated using Bernoulli’s equation: (1/2)u1² + gz1 + p1/ρ = (1/2)u2² + gz2 + p2/ρ + ΔP. Here, u1 is the flow velocity of the exhaust gas at the base of the chimney (I won’t use subscripts here; therefore, u1² should be understood as the square of u1, and similarly for u2²). Who would write it? Please tell me. ) z1—is the elevation at the base of the chimney; it is taken as z1=0. p1—is the pressure at the base of the chimney, which is the negative value of the suction force, and can be determined based on the total resistance from the air inlet to the base of the chimney. u2: the exhaust gas flow velocity at the chimney outlet, typically ranging from 3 to 4 m/s. z2: the elevation at the chimney outlet, that is, the height of the chimney; z2 = H. p2: the pressure at the chimney outlet, which is the external atmospheric pressure, with p2 set to 0. ΔP: the resistance encountered by the chimney. Based on these conditions, the flow velocity u1 of the exhaust gas at the base of the chimney can be calculated. By combining this with the exhaust gas volume Q = (π/4) × D × D, the diameter D at the base of the chimney can be determined.
Reply to 4# wangshaobo: Thank you for your patient answers. Are these all from the book \"Coking Science\"? The bottom diameter has now been found; thanks again!
OP, are my calculation results the same as the values you found? I helped you solve the problem, but you don’t even give me some points.
Reply to 6# wangshaobo: To be honest, everything you mentioned can be found verbatim in the literature on coking. If I only needed what you said, there would be no need to post a thread at all; but thanks for your enthusiasm!
This post was last edited by www.jsycyn.com on 2012-3-22 at 11:54. First of all, I would like to ask the original poster what structure the 70m chimney has. According to the national standard catalogs, brick chimneys come in heights of 30m, 40m, 50m, and 60m, while the catalogs for reinforced concrete chimneys specify heights of 60m, 80m, and 100m... For chimneys with different structures, their diameter slopes also vary; therefore, the following analysis will help you understand this, so you can compare it on your own! 1. Brick chimneys: For brick chimneys, the radius increases by 0.025 m and the diameter increases by 0.05 m for every 1 m downward. Therefore, the diameter at the bottom is 3 + 70×0.05 = 6.5 m.
2. Concrete chimneys: For concrete chimneys, the radius increases by 0.02 m and the diameter increases by 0.04 m for every 1 m downward. Thus, the diameter at the bottom is 3 + 70×0.04 = 5.8 m. I work in the field of chimney construction, repair, and anti-corrosion treatment, so I have considerable experience with chimneys. I hope this straightforward method will be useful to you.
2. Concrete chimneys: For concrete chimneys, the radius increases by 0.02 m and the diameter increases by 0.04 m for every 1 m downward. Thus, the diameter at the bottom is 3 + 70×0.04 = 5.8 m. I work in the field of chimney construction, repair, and anti-corrosion treatment, so I have considerable experience with chimneys. I hope this straightforward method will be useful to you.