Term information
(mean velocity equation) The purpose of the currently accepted equations by Hemeon and the American Conference of Governmental Industrial Hygienists (ACGIH) is to estimate the plume volumetric flow (Q) [The volumetric flow above a heated source is defined as the product of the plume mean velocity and area (ACGIH, 1998; Hemeon, 1999).] at which heat and fine particle effluents are being introduced to the face of the engineering control (i.e. receiving hood). Determining the plume flow is of critical interest for two reasons: (1) it must provide adequate control of the effluent to prevent spillage back into the workplace air; (2) it should be calculated as accurately as possible to prevent overventilating the process, as this wastes conditioned indoor air. Accuracy of the flow estimation is important, as results from a laboratory study to determine the accuracy of Hemeon's flow equation indicated that this equation overestimates the flow above heated sources leading to excess process ventilation (Siebert and Fraser, 1973). source: JOHN L. McKERNAN, MICHAEL J. ELLENBECKER, CHRISTINA A. HOLCROFT and MARTIN R. PETERSEN: Evaluation of a Proposed Velocity Equation for Improved Exothermic Process Control. Ann Occup Hyg (2007) 51 (4): 357-369. doi: 10.1093/annhyg/mem016 - First published online: May 22, 2007 Uquer_H (FPM) = 37 / H_H^0.29 * (hH / 60 * AB T)^0.33 Uquer_H (m s^-1) = 5.08 x 10^-3 [37 / H_H^0.29 * (hH / 60 * AB T)^0.33] = 0.19 / H_H^0.29 * (hH / 60 * AB T)^0.33 hH = Natural convection heat loss coefficient for vertical plates; 0.30( T)0.25 (BTU hr 1 AB = Area of entire cylinder emitting heat; (3.28RS)2 + 21.5 LRS (ft2; L and RS in m) T = Excess temperature; (Ts http://annhyg.oxfordjournals.org/content/51/4/357.long
<math xmlns="http://www.w3.org/1998/Math/MathML" display="block"> <mrow> <mrow> <msub> <mover accent="true"> <mi>U</mi> <mo>¯</mo> </mover> <mi>H</mi> </msub> <mo>⁢</mo> <mfenced close=")" open="("> <mrow> <mi>F</mi> <mo>⁢</mo> <mi>P</mi> <mo>⁢</mo> <mi>M</mi> </mrow> </mfenced> </mrow> <mo>=</mo> <mrow> <mrow> <mn>37</mn> <mo>/</mo> <msubsup> <mi>H</mi> <mi>H</mi> <mn>0.29</mn> </msubsup> </mrow> <mo>*</mo> <msup> <mfenced close=")" open="("> <mrow> <mrow> <msub> <mi>h</mi> <mi>H</mi> </msub> <mo>/</mo> <mn>60</mn> </mrow> <mo>*</mo> <mrow> <msub> <mi>A</mi> <mi>B</mi> </msub> <mo>⁢</mo> <mi>Δ</mi> <mo>⁢</mo> <mi>T</mi> </mrow> </mrow> </mfenced> <mn>0.33</mn> </msup> </mrow> </mrow> </math>
<math xmlns="http://www.w3.org/1998/Math/MathML" display="block"> <mrow> <mrow> <msub> <mover accent="true"> <mi>U</mi> <mo>¯</mo> </mover> <mi>H</mi> </msub> <mo>⁢</mo> <mfenced close=")" open="("> <mrow> <mi>m</mi> <mo>⁢</mo> <msup> <mi>s</mi> <mn>-1</mn> </msup> </mrow> </mfenced> </mrow> <mo>=</mo> <mrow> <mn>5.08</mn> <mo>⁢</mo> <mi>x</mi> <mo>⁢</mo> <msup> <mn>10</mn> <mn>-3</mn> </msup> <mo>⁢</mo> <mfenced close="]" open="["> <mrow> <mrow> <mn>37</mn> <mo>/</mo> <msubsup> <mi>H</mi> <mi>H</mi> <mn>0.29</mn> </msubsup> </mrow> <mo>*</mo> <msup> <mfenced close=")" open="("> <mrow> <mrow> <mrow> <mi>h</mi> <mo>⁢</mo> <mi>H</mi> </mrow> <mo>/</mo> <mn>60</mn> </mrow> <mo>*</mo> <mrow> <mi>A</mi> <mo>⁢</mo> <mi>B</mi> <mo>⁢</mo> <mi>Δ</mi> <mo>⁢</mo> <mi>T</mi> </mrow> </mrow> </mfenced> <mn>0.33</mn> </msup> </mrow> </mfenced> </mrow> <mo>=</mo> <mrow> <mrow> <mn>0.19</mn> <mo>/</mo> <msubsup> <mi>H</mi> <mi>H</mi> <mn>0.29</mn> </msubsup> </mrow> <mo>*</mo> <msup> <mfenced close=")" open="("> <mrow> <mrow> <mrow> <mi>h</mi> <mo>⁢</mo> <mi>H</mi> </mrow> <mo>/</mo> <mn>60</mn> </mrow> <mo>*</mo> <mrow> <mi>A</mi> <mo>⁢</mo> <mi>B</mi> <mo>⁢</mo> <mi>Δ</mi> <mo>⁢</mo> <mi>T</mi> </mrow> </mrow> </mfenced> <mn>0.33</mn> </msup> </mrow> </mrow> </math>
\overline {U}_H (FPM) = 37 / H_H^0.29 * (h_H / 60 * A_B \Delta T)^0.33
\overline {U}_H (m s^{-1}) = 5.08 x 10^{-3} [37 / H_H^0.29 * (hH / 60 * AB \Delta T)^0.33] = 0.19 / H_H^0.29 * (hH / 60 * AB \Delta T)^0.33
<math xmlns="http://www.w3.org/1998/Math/MathML" display="block" id="Hemeon equation1"> <mrow> <msub> <mrow> <mover> <mi>U</mi> <mo>¯</mo> </mover> </mrow> <mi>H</mi> </msub> <mfenced> <mrow> <mi>F</mi> <mi>P</mi> <mi>M</mi> </mrow> </mfenced> <mo>=</mo> <mn>37</mn> <mo>/</mo> <msubsup> <mi>H</mi> <mrow> <mi>H</mi> </mrow> <mn>0.29</mn> </msubsup> <mo>·</mo> <msup> <mfenced> <mrow> <msub> <mi>h</mi> <mi>H</mi> </msub> <mo>/</mo> <mn>60</mn> <mo>·</mo> <msub> <mi>A</mi> <mi>B</mi> </msub> <mi>Δ</mi> <mi>T</mi> </mrow> </mfenced> <mn>0.33</mn> </msup> </mrow> </math>
<math xmlns="http://www.w3.org/1998/Math/MathML" display="block" id="Hemeon equation2"> <mrow> <msub> <mrow> <mover> <mi>U</mi> <mo>¯</mo> </mover> </mrow> <mi>H</mi> </msub> <mfenced> <mrow> <mi>m</mi> <msup> <mi>s</mi> <mfenced> <mrow> <mo>-</mo> <mn>1</mn> </mrow> </mfenced> </msup> </mrow> </mfenced> <mo>=</mo> <mn>5.08</mn> <mo>·</mo> <msup> <mn>10</mn> <mfenced> <mrow> <mo>-</mo> <mn>3</mn> </mrow> </mfenced> </msup> <mo>[</mo> <mrow> <mn>37</mn> <mo>/</mo> <msubsup> <mi>H</mi> <mrow> <mi>H</mi> </mrow> <mn>0.29</mn> </msubsup> </mrow> <mo>·</mo> <mrow> <msup> <mfenced> <mrow> <msub> <mi>h</mi> <mi>H</mi> </msub> <mo>/</mo> <mn>60</mn> <mo>·</mo> <msub> <mi>A</mi> <mi>B</mi> </msub> <mi>Δ</mi> <mi>T</mi> </mrow> </mfenced> <mn>0.33</mn> </msup> </mrow> <mo>]</mo> <mo>=</mo> <mn>0.19</mn> <mo>/</mo> <msubsup> <mi>H</mi> <mrow> <mi>H</mi> </mrow> <mn>0.29</mn> </msubsup> <mo>·</mo> <msup> <mfenced> <mrow> <msub> <mi>h</mi> <mi>H</mi> </msub> <mo>/</mo> <mn>60</mn> <mo>·</mo> <msub> <mi>A</mi> <mi>B</mi> </msub> <mi>Δ</mi> <mi>T</mi> </mrow> </mfenced> <mn>0.33</mn> </msup> </mrow> </math>
Term relations
- equation for mean
- describes some motion
- has_variable some (
variable and
is_about some temperature) - has_variable some (
variable and
is_about some area)