Attachment 182690 Details for Bug 106866 – html file which should be showing square root symbol

html file which should be showing square root symbol

mathml.html (text/html), 4.71 KB, created by Irfan Omair on 2013-01-14 20:50:12 PST

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Creator: Irfan Omair

Created: 2013-01-14 20:50:12 PST

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obsolete

><!DOCTYPE html>
><html>
><head>
><title>New concepts in commerce 3rd ed.</title>
><meta charset="utf-8"/>
><meta name="viewport" content="width=1024, height=768"/>
><link rel="stylesheet" href="css/fixed-css.css" type="text/css"/>
></head>
><body>
><div class="galley-rw">
><div class="body-rw Part-rw">
><div class="pgst">
><p>The ratio <i>&#x03C4;</i><sub>b</sub>/<i>&#x03C1;</i> has the same dimension as the square of a velocity, and for this reason, it is customary to define</p>
><table><tr><td class="eqn-cell-center"><div style="height: 45px;" class="math-table"><math display="block"><mrow><msub><mi>u</mi><mo>*</mo></msub><mo>=</mo><msqrt><mrow><mfrac><mrow><msub><mi>&#x03C4;</mi><mtext>b</mtext></msub></mrow><mi>&#x03C1;</mi></mfrac></mrow></msqrt><mo>,</mo></mrow></math></div></td><td class="eqn-cell-right"><span class="mtlabel">(8.1)</span></td></tr></table>
><p>which is called the <i>friction velocity</i> or <i>turbulent velocity</i>. Physically, its value is related to the orbital velocity of the vortices that create the cross-flow exchange of particles and the momentum transfer.</p>
><p>The velocity structure thus obeys a relation of the form <i>u</i>(<i>z</i>) = <i>F</i>(<i>u</i><sub>*</sub>, <i>&#x03BD;</i>, <i>z</i>), and further use of dimensional analysis reduces it to a function of a single variable:</p>
><table><tr><td class="eqn-cell-center"><div style="height: 45px;" class="math-table"><math display="block"><mrow><mfrac><mrow><mi>u</mi><mo stretchy='false'>(</mo><mi>z</mi><mo stretchy='false'>)</mo></mrow><mrow><msub><mi>u</mi><mo>*</mo></msub></mrow></mfrac><mo>=</mo><mi>F</mi><mrow><mo>(</mo><mrow><mfrac><mrow><msub><mi>u</mi><mo>*</mo></msub><mi>z</mi></mrow><mi>&#x03BD;</mi></mfrac></mrow><mo>)</mo></mrow><mo>.</mo></mrow></math></div></td><td class="eqn-cell-right"><span class="mtlabel">(8.2)</span></td></tr></table>
><p>In the presence of rotation, the Coriolis parameter enters the formalism, and the preceding function depends on two variables:</p>
><table><tr><td class="eqn-cell-center"><div style="height: 45px;" class="math-table"><math display="block"><mrow><mfrac><mrow><mi>u</mi><mo stretchy='false'>(</mo><mi>z</mi><mo stretchy='false'>)</mo></mrow><mrow><msub><mi>u</mi><mo>*</mo></msub></mrow></mfrac><mo>=</mo><mi>F</mi><mrow><mo>(</mo><mrow><mfrac><mrow><msub><mi>u</mi><mo>*</mo></msub><mi>z</mi></mrow><mi>&#x03BD;</mi></mfrac><mo>,</mo><mfrac><mrow><mi>f</mi><mi>z</mi></mrow><mrow><msub><mi>u</mi><mo>*</mo></msub></mrow></mfrac></mrow><mo>)</mo></mrow><mtext>&#x200B;</mtext><mo>.</mo></mrow></math></div></td><td class="eqn-cell-right"><span class="mtlabel">(8.3)</span></td></tr></table>
><h2 class="bhead"><span class="table-cell">8.1.1</span><span class="table-cell-1">Logarithmic Profile</span></h2>
><p>The observational determination of the function <i>F</i> in the absence of rotation has been repeated countless times, yielding the same results every time, and it suffices here to provide a single report (Fig. 8.1). When the velocity ratio <i>u</i>/<i>u</i><sub>*</sub> is plotted versus the logarithm of the dimensionless distance <i>u</i><sub>*</sub><i>z</i>/&#x03BD;, not only do all the points coalesce onto a single curve, confirming that there is indeed no other variable to be invoked, but the curve also behaves as a straight line over a range of two orders of magnitude (from <i>u</i><sub>*</sub><i>z</i>/&#x03BD; between 10<sup>1</sup> and 10<sup>3</sup>).</p>
><p>If the velocity is linearly dependent on the logarithm of the distance, then we can write for this portion of the velocity profile:</p>
><div class="equation"><div style="height: 45px;" class="math-table"><math display="block"><mrow><mfrac><mrow><mi>u</mi><mo stretchy='false'>(</mo><mi>z</mi><mo stretchy='false'>)</mo></mrow><mrow><msub><mi>u</mi><mo>*</mo></msub></mrow></mfrac><mo>=</mo><mi>A</mi><mi>ln</mi><mfrac><mrow><msub><mi>u</mi><mo>*</mo></msub><mi>z</mi></mrow><mi>&#x03BD;</mi></mfrac><mo>+</mo><mi>B</mi><mo>.</mo></mrow></math></div></div>
><p>Numerous experimental determinations of the constants <i>A</i> and <i>B</i> provide <i>A</i> = 2.44 and <i>B</i> = 5.2 within a 5% error (Pope, 2000). Tradition has it to write</p>
><p>the function as:</p>
><table><tr><td class="eqn-cell-center"><div style="height: 45px;" class="math-table"><math display="block"><mrow><mi>u</mi><mo stretchy='false'>(</mo><mi>z</mi><mo stretchy='false'>)</mo><mo>=</mo><mfrac><mrow><msub><mi>u</mi><mo>*</mo></msub></mrow><mi mathvariant='script'>K</mi></mfrac><mi>ln</mi><mfrac><mrow><msub><mi>u</mi><mo>*</mo></msub><mi>z</mi></mrow><mi>&#x03BD;</mi></mfrac><mo>+</mo><mn>5.2</mn><msub><mi>u</mi><mo>*</mo></msub><mo>,</mo></mrow></math></div></td><td class="eqn-cell-right"><span class="mtlabel">(8.4)</span></td></tr></table>
></div>
></div>
></div>
></body>
></html>

<!DOCTYPE html>
<html>
<head>
<title>New concepts in commerce 3rd ed.</title>
<meta charset="utf-8"/>
<meta name="viewport" content="width=1024, height=768"/>
<link rel="stylesheet" href="css/fixed-css.css" type="text/css"/>
</head>
<body>
<div class="galley-rw">
<div class="body-rw Part-rw">
<div class="pgst">
<p>The ratio <i>&#x03C4;</i><sub>b</sub>/<i>&#x03C1;</i> has the same dimension as the square of a velocity, and for this reason, it is customary to define</p>
<table><tr><td class="eqn-cell-center"><div style="height: 45px;" class="math-table"><math display="block"><mrow><msub><mi>u</mi><mo>*</mo></msub><mo>=</mo><msqrt><mrow><mfrac><mrow><msub><mi>&#x03C4;</mi><mtext>b</mtext></msub></mrow><mi>&#x03C1;</mi></mfrac></mrow></msqrt><mo>,</mo></mrow></math></div></td><td class="eqn-cell-right"><span class="mtlabel">(8.1)</span></td></tr></table>
<p>which is called the <i>friction velocity</i> or <i>turbulent velocity</i>. Physically, its value is related to the orbital velocity of the vortices that create the cross-flow exchange of particles and the momentum transfer.</p>
<p>The velocity structure thus obeys a relation of the form <i>u</i>(<i>z</i>) = <i>F</i>(<i>u</i><sub>*</sub>, <i>&#x03BD;</i>, <i>z</i>), and further use of dimensional analysis reduces it to a function of a single variable:</p>
<table><tr><td class="eqn-cell-center"><div style="height: 45px;" class="math-table"><math display="block"><mrow><mfrac><mrow><mi>u</mi><mo stretchy='false'>(</mo><mi>z</mi><mo stretchy='false'>)</mo></mrow><mrow><msub><mi>u</mi><mo>*</mo></msub></mrow></mfrac><mo>=</mo><mi>F</mi><mrow><mo>(</mo><mrow><mfrac><mrow><msub><mi>u</mi><mo>*</mo></msub><mi>z</mi></mrow><mi>&#x03BD;</mi></mfrac></mrow><mo>)</mo></mrow><mo>.</mo></mrow></math></div></td><td class="eqn-cell-right"><span class="mtlabel">(8.2)</span></td></tr></table>
<p>In the presence of rotation, the Coriolis parameter enters the formalism, and the preceding function depends on two variables:</p>
<table><tr><td class="eqn-cell-center"><div style="height: 45px;" class="math-table"><math display="block"><mrow><mfrac><mrow><mi>u</mi><mo stretchy='false'>(</mo><mi>z</mi><mo stretchy='false'>)</mo></mrow><mrow><msub><mi>u</mi><mo>*</mo></msub></mrow></mfrac><mo>=</mo><mi>F</mi><mrow><mo>(</mo><mrow><mfrac><mrow><msub><mi>u</mi><mo>*</mo></msub><mi>z</mi></mrow><mi>&#x03BD;</mi></mfrac><mo>,</mo><mfrac><mrow><mi>f</mi><mi>z</mi></mrow><mrow><msub><mi>u</mi><mo>*</mo></msub></mrow></mfrac></mrow><mo>)</mo></mrow><mtext>&#x200B;</mtext><mo>.</mo></mrow></math></div></td><td class="eqn-cell-right"><span class="mtlabel">(8.3)</span></td></tr></table>
<h2 class="bhead"><span class="table-cell">8.1.1</span><span class="table-cell-1">Logarithmic Profile</span></h2>
<p>The observational determination of the function <i>F</i> in the absence of rotation has been repeated countless times, yielding the same results every time, and it suffices here to provide a single report (Fig. 8.1). When the velocity ratio <i>u</i>/<i>u</i><sub>*</sub> is plotted versus the logarithm of the dimensionless distance <i>u</i><sub>*</sub><i>z</i>/&#x03BD;, not only do all the points coalesce onto a single curve, confirming that there is indeed no other variable to be invoked, but the curve also behaves as a straight line over a range of two orders of magnitude (from <i>u</i><sub>*</sub><i>z</i>/&#x03BD; between 10<sup>1</sup> and 10<sup>3</sup>).</p>
<p>If the velocity is linearly dependent on the logarithm of the distance, then we can write for this portion of the velocity profile:</p>
<div class="equation"><div style="height: 45px;" class="math-table"><math display="block"><mrow><mfrac><mrow><mi>u</mi><mo stretchy='false'>(</mo><mi>z</mi><mo stretchy='false'>)</mo></mrow><mrow><msub><mi>u</mi><mo>*</mo></msub></mrow></mfrac><mo>=</mo><mi>A</mi><mi>ln</mi><mfrac><mrow><msub><mi>u</mi><mo>*</mo></msub><mi>z</mi></mrow><mi>&#x03BD;</mi></mfrac><mo>+</mo><mi>B</mi><mo>.</mo></mrow></math></div></div>
<p>Numerous experimental determinations of the constants <i>A</i> and <i>B</i> provide <i>A</i> = 2.44 and <i>B</i> = 5.2 within a 5% error (Pope, 2000). Tradition has it to write</p>
<p>the function as:</p>
<table><tr><td class="eqn-cell-center"><div style="height: 45px;" class="math-table"><math display="block"><mrow><mi>u</mi><mo stretchy='false'>(</mo><mi>z</mi><mo stretchy='false'>)</mo><mo>=</mo><mfrac><mrow><msub><mi>u</mi><mo>*</mo></msub></mrow><mi mathvariant='script'>K</mi></mfrac><mi>ln</mi><mfrac><mrow><msub><mi>u</mi><mo>*</mo></msub><mi>z</mi></mrow><mi>&#x03BD;</mi></mfrac><mo>+</mo><mn>5.2</mn><msub><mi>u</mi><mo>*</mo></msub><mo>,</mo></mrow></math></div></td><td class="eqn-cell-right"><span class="mtlabel">(8.4)</span></td></tr></table>
</div>
</div>
</div>
</body>
</html>

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Attachments on bug 106866: 182690 | 182691 | 233523