tag:blogger.com,1999:blog-4115807457737539772024-03-05T19:50:48.071-08:00BNP10303 Fluid MechanicsBASIC EQUATION IN FLUID MECHANICSizzmirza mohsinhttp://www.blogger.com/profile/08473641161172340998noreply@blogger.comBlogger5125tag:blogger.com,1999:blog-411580745773753977.post-47955385654462578642018-05-10T22:07:00.002-07:002018-05-10T22:08:32.931-07:00PRESSURE<div class="MsoNormal" style="line-height: 150%; margin-bottom: 8pt; text-align: center;">
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<b><span style="font-family: "times new roman" , serif; font-size: 12.0pt; line-height: 150%;">Pressure Terminology <o:p></o:p></span></b></div>
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<span class="mord"><i><span lang="EN-US" style="background: white; border: none 1.0pt; color: #21242c; font-family: "katex_math" , serif; font-size: 17.5pt; line-height: 150%; padding: 0cm;">P</span></i></span><span class="mrel"><span lang="EN-US" style="background: white; border: none 1.0pt; color: #21242c; font-size: 17.5pt; line-height: 150%; padding: 0cm;">=</span></span><span class="mord"><i><span lang="EN-US" style="background: white; border: none 1.0pt; color: #21242c; font-family: "katex_math" , serif; font-size: 17.5pt; line-height: 150%; padding: 0cm;">ρgh</span></i></span><b><span style="font-family: "times new roman" , serif; font-size: 12.0pt; line-height: 150%;"><o:p></o:p></span></b></div>
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<span style="font-family: "times new roman" , serif; font-size: 12.0pt; line-height: 150%;">There are three different kinds of pressure reported in the literature,
and it is important to know the terminology:<o:p></o:p></span></div>
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<!--[if !supportLists]--><span style="font-family: "times new roman" , serif; font-size: 12.0pt; line-height: 150%;">1.<span style="font-family: "times new roman"; font-size: 7pt; font-stretch: normal; line-height: normal;">
</span></span><!--[endif]--><b><span style="font-family: "times new roman" , serif; font-size: 12.0pt; line-height: 150%;">Absolute pressure</span></b><span style="font-family: "times new roman" , serif; font-size: 12.0pt; line-height: 150%;"> is measured relative to
absolute zero on the pressure scale, which is a perfect vacuum. (Absolute
pressure can never be negative.) Absolute pressure is indicated by P and is
identical to the familiar thermodynamic pressure.<o:p></o:p></span></div>
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<!--[if !supportLists]--><span style="font-family: "times new roman" , serif; font-size: 12.0pt; line-height: 150%;">2.<span style="font-family: "times new roman"; font-size: 7pt; font-stretch: normal; line-height: normal;">
</span></span><!--[endif]--><b><span style="font-family: "times new roman" , serif; font-size: 12.0pt; line-height: 150%;">Gage pressure </span></b><span style="font-family: "times new roman" , serif; font-size: 12.0pt; line-height: 150%;">(sometimes written as "gauge
pressure") is measured relative to the local atmospheric pressure. Gage
pressure is thus zero when the pressure is the same as atmospheric pressure.
(It is possible to have negative gage pressure.) Gage pressure is indicated by
Pg and is related to absolute pressure as follows: Pg = P - Pa, where pa is the
local atmospheric pressure.<o:p></o:p></span></div>
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<!--[if !supportLists]--><span style="font-family: "times new roman" , serif; font-size: 12.0pt; line-height: 150%;">3.<span style="font-family: "times new roman"; font-size: 7pt; font-stretch: normal; line-height: normal;">
</span></span><!--[endif]--><b><span style="font-family: "times new roman" , serif; font-size: 12.0pt; line-height: 150%;">Vacuum pressure</span></b><span style="font-family: "times new roman" , serif; font-size: 12.0pt; line-height: 150%;"> is also measured relative
to the local atmospheric pressure, but is used when the gage pressure is
negative, i.e. when the absolute pressure falls below the local atmospheric
pressure. (Positive vacuum pressure means that the gage pressure is negative.)
Vacuum pressure is indicated by Pvacuum and is related to absolute pressure as
follows: Pvacuum = Pa - P, where pa is the local atmospheric pressure.<o:p></o:p></span></div>
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<span class="mord"><i><span lang="EN-US" style="border: none 1.0pt; font-family: "katex_math" , serif; font-size: 17.5pt; line-height: 115%; padding: 0cm;">P</span><span lang="EN-US" style="border: none 1.0pt; font-family: "katex_math" , serif; font-size: 11.0pt; line-height: 115%; padding: 0cm;">total</span></i></span><span class="vlist-s"><span lang="EN-US" style="border: none 1.0pt; font-family: "inherit" , serif; font-size: 1.0pt; line-height: 115%; padding: 0cm;"></span></span><span class="mrel"><span lang="EN-US" style="border: none 1.0pt; font-family: "inherit" , serif; font-size: 17.5pt; line-height: 115%; padding: 0cm;">=</span></span><span class="mord"><i><span lang="EN-US" style="border: none 1.0pt; font-family: "katex_math" , serif; font-size: 17.5pt; line-height: 115%; padding: 0cm;">ρgh</span></i></span><span class="mbin"><span lang="EN-US" style="border: none 1.0pt; font-family: "inherit" , serif; font-size: 17.5pt; line-height: 115%; padding: 0cm;">+</span></span><span class="mord"><i><span lang="EN-US" style="border: none 1.0pt; font-family: "katex_math" , serif; font-size: 17.5pt; line-height: 115%; padding: 0cm;">P</span><span lang="EN-US" style="background: white; border: none 1.0pt; color: #21242c; font-family: "katex_math" , serif; font-size: 18.0pt; line-height: 115%; padding: 0cm;">atm</span></i></span><span class="vlist-s"><span lang="EN-US" style="background: white; border: none 1.0pt; color: #21242c; font-family: "inherit" , serif; font-size: 1.0pt; line-height: 115%; padding: 0cm;"></span></span><br />
<span class="vlist-s"><span lang="EN-US" style="background: white; border: none 1.0pt; color: #21242c; font-family: "inherit" , serif; font-size: 1.0pt; line-height: 115%; padding: 0cm;"><br /></span></span></div>
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<b><span lang="EN-US" style="font-family: "times new roman" , serif; font-size: 12.0pt; line-height: 150%;">EXAMPLE<o:p></o:p></span></b></div>
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<!--[if !supportLists]--><span lang="EN-US" style="font-family: "times new roman" , serif; font-size: 12.0pt; line-height: 150%;"><span style="mso-list: Ignore;">1.<span style="font: 7.0pt "Times New Roman";">
</span></span></span><!--[endif]--><span lang="EN-US" style="font-family: "times new roman" , serif; font-size: 12.0pt; line-height: 150%;">Pressure
acting in water at depth <span style="mso-bidi-font-style: italic;">1 m</span>.
</span><span lang="EN-US" style="font-family: "times new roman" , serif; font-size: 12.0pt; line-height: 150%;">The <span class="MsoHyperlink"><span style="color: windowtext; text-decoration: none; text-underline: none;"><a href="https://www.engineeringtoolbox.com/water-density-specific-weight-d_595.html" title="density water"><span style="color: windowtext; text-decoration: none; text-underline: none;">density of water</span></a></span></span> at <span style="mso-bidi-font-style: italic;">4<sup>o</sup>C</span> is <span style="mso-bidi-font-style: italic;">1000 kg/m<sup>3</sup></span>. The pressure
acting in water at <span style="mso-bidi-font-style: italic;">1 m</span> can
be calculated as<span style="mso-bidi-font-weight: bold;"><o:p></o:p></span></span></div>
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<b><span lang="EN-US" style="font-family: "times new roman" , serif; font-size: 12.0pt; line-height: 150%;">Solution:<o:p></o:p></span></b></div>
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<span lang="EN-US" style="font-family: "times new roman" , serif; font-size: 12.0pt; line-height: 150%;">p = ρ g h </span><span lang="EN-US" style="font-family: "times new roman" , serif; font-size: 12.0pt; line-height: 150%;"><o:p></o:p></span></div>
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<span lang="EN-US" style="font-family: "times new roman" , serif; font-size: 12.0pt; line-height: 150%;"> = (1000 kg/m<sup>3</sup>) (9.81 m/s<sup>2</sup>) (1
m) </span><span lang="EN-US" style="font-family: "times new roman" , serif; font-size: 12.0pt; line-height: 150%;"><o:p></o:p></span></div>
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<span lang="EN-US" style="font-family: "times new roman" , serif; font-size: 12.0pt; line-height: 150%;"> = 9810 Pa<o:p></o:p></span></div>
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<!--[if !supportLists]--><span lang="EN-US" style="font-family: "times new roman" , serif; font-size: 12.0pt; line-height: 150%;"><span style="mso-list: Ignore;">2.<span style="font: 7.0pt "Times New Roman";">
</span></span></span><!--[endif]--><span lang="EN-US" style="font-family: "times new roman" , serif; font-size: 12.0pt; line-height: 150%;">Pressure
acting in water at depth <span style="mso-bidi-font-style: italic;">3 ft. </span></span><span lang="EN-US" style="font-family: "times new roman" , serif; font-size: 12.0pt; line-height: 150%;">The <span class="MsoHyperlink"><span style="color: windowtext; text-decoration: none; text-underline: none;"><a href="https://www.engineeringtoolbox.com/water-density-specific-weight-d_595.html" title="density water"><span style="color: windowtext; text-decoration: none; text-underline: none;">density of water</span></a></span></span> at <span style="mso-bidi-font-style: italic;">32<sup>o</sup>F</span> is <span style="mso-bidi-font-style: italic;">1.940 slugs/ft<sup>3</sup></span>. The
pressure acting in water at <span style="mso-bidi-font-style: italic;">3
ft</span> can be calculated as<span style="mso-bidi-font-weight: bold;"><o:p></o:p></span></span></div>
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<b style="mso-bidi-font-weight: normal;"><span lang="EN-US" style="font-family: "times new roman" , serif; font-size: 12.0pt; line-height: 150%;">Solution:<o:p></o:p></span></b></div>
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<span lang="EN-US" style="font-family: "times new roman" , serif; font-size: 12.0pt; line-height: 150%;">p = ρ g h</span><span lang="EN-US" style="font-family: "times new roman" , serif; font-size: 12.0pt; line-height: 150%;"><o:p></o:p></span></div>
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<span lang="EN-US" style="font-family: "times new roman" , serif; font-size: 12.0pt; line-height: 150%;"> = (1.940 slugs/ft<sup>3</sup>) (32.17405 ft/s<sup>2</sup>) (3
ft) </span><span lang="EN-US" style="font-family: "times new roman" , serif; font-size: 12.0pt; line-height: 150%;"><o:p></o:p></span></div>
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<span lang="EN-US" style="font-family: "times new roman" , serif; font-size: 12.0pt; line-height: 150%;"> = 187.3 lb<sub>f</sub>/ft<sup>2</sup> (psf)</span><span lang="EN-US" style="font-family: "times new roman" , serif; font-size: 12.0pt; line-height: 150%;"><o:p></o:p></span></div>
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<span lang="EN-US" style="font-family: "times new roman" , serif; font-size: 12.0pt; line-height: 150%;"> = 1.3 lb<sub>f</sub>/in<sup>2</sup> (psi)</span><span lang="EN-US" style="font-family: "times new roman" , serif; font-size: 12.0pt; line-height: 150%;"><o:p></o:p></span></div>
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izzmirza mohsinhttp://www.blogger.com/profile/08473641161172340998noreply@blogger.comtag:blogger.com,1999:blog-411580745773753977.post-53193605966068446052018-05-07T10:04:00.002-07:002018-05-07T10:27:25.520-07:00CONCLUSION<div class="separator" style="clear: both; text-align: justify;">
Pressure, Archimedes and Bernoulli and the continuity equations are the most fundamental equations in Fluid Mechanics. They will be used very frequently in the next chapter after this. In chapter Four which is Basic Equations in Fluid Mechanic, either the Bernoulli equation or the continuity equation is used together with the mass and momentum equations to find out the torques and forces acting on fluid systems. So, it is very important for all of us to understand this equation. To wrap up this chapter, we can conclude that,</div>
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Archimedes Formula</div>
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<span lang="EN-US" style="font-size: 12.0pt; font-weight: normal; line-height: 150%; mso-bidi-font-weight: bold;">Volume Flow Rate<o:p></o:p></span></h3>
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<span lang="EN-US" style="font-family: "times new roman" , serif; font-size: 12.0pt; line-height: 150%;">Equation of Continuity<o:p></o:p></span></div>
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<span style="font-family: "times new roman" , serif; font-size: 12pt; text-align: center;">Bernoullis’s Equation</span></div>
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REFERENCES:</div>
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<!--[if !supportLists]--><span style="font-family: Calibri; font-size: 11.0000pt; mso-bidi-font-family: 'Times New Roman'; mso-fareast-font-family: SimSun;">1. </span><!--[endif]--><a href="http://www.softschools.com/formulas/physics/buoyancy_formula/28/"><u><span class="15" style="color: blue; font-family: Calibri;">http://www.softschools.com/formulas/physics/buoyancy_formula/28/</span></u></a><span style="font-family: Calibri; font-size: 11.0000pt; mso-bidi-font-family: 'Times New Roman'; mso-fareast-font-family: SimSun; mso-spacerun: 'yes';"><o:p></o:p></span></div>
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<!--[if !supportLists]--><span style="font-family: Calibri; font-size: 11.0000pt; mso-bidi-font-family: 'Times New Roman'; mso-fareast-font-family: SimSun;">2. </span><!--[endif]--><span style="font-family: Calibri; font-size: 11.0000pt; mso-bidi-font-family: 'Times New Roman'; mso-fareast-font-family: SimSun; mso-spacerun: 'yes';">Acott, Chris (1999). "The diving "Law-ers": A brief resume of their lives". South Pacific Underwater Medicine Society journal. 29 (1). ISSN 0813-1988. OCLC 16986801. Retrieved 2009-06-13.</span><span style="font-family: Calibri; font-size: 11.0000pt; mso-bidi-font-family: 'Times New Roman'; mso-fareast-font-family: SimSun; mso-spacerun: 'yes';"><o:p></o:p></span></div>
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<!--[if !supportLists]--><span style="font-family: Calibri; font-size: 11.0000pt; mso-bidi-font-family: 'Times New Roman'; mso-fareast-font-family: SimSun;">3. </span><!--[endif]--><span style="font-family: Calibri; font-size: 11.0000pt; mso-bidi-font-family: 'Times New Roman'; mso-fareast-font-family: SimSun; mso-spacerun: 'yes';">"Floater clustering in a standing wave: Capillarity effects drive hydrophilic or hydrophobic particles to congregate at specific points on a wave" (PDF). 2005-06-23.</span><span style="font-family: Calibri; font-size: 11.0000pt; mso-bidi-font-family: 'Times New Roman'; mso-fareast-font-family: SimSun; mso-spacerun: 'yes';"><o:p></o:p></span></div>
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<!--[if !supportLists]--><span style="font-family: Calibri; font-size: 11.0000pt; mso-bidi-font-family: 'Times New Roman'; mso-fareast-font-family: SimSun;">4. </span><!--[endif]--><span style="font-family: Calibri; font-size: 11.0000pt; mso-bidi-font-family: 'Times New Roman'; mso-fareast-font-family: SimSun; mso-spacerun: 'yes';">"Archimedes’s principle gets updated". R. Mark Wilson, Physics Today 65(9), 15 (2012); doi:10.1063/PT.3.1701</span><span style="font-family: Calibri; font-size: 11.0000pt; mso-bidi-font-family: 'Times New Roman'; mso-fareast-font-family: SimSun; mso-spacerun: 'yes';"><o:p></o:p></span></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: 21.2500pt; mso-char-indent-count: 0.0000; mso-list: l0 level1 lfo1; mso-para-margin-left: 0.0000gd; text-indent: -21.2500pt;">
<!--[if !supportLists]--><span style="font-family: Calibri; font-size: 11.0000pt; mso-bidi-font-family: 'Times New Roman'; mso-fareast-font-family: SimSun;">5. </span><!--[endif]--><span style="font-family: Calibri; font-size: 11.0000pt; mso-bidi-font-family: 'Times New Roman'; mso-fareast-font-family: SimSun; mso-spacerun: 'yes';">"The works of Archimedes". p. 257. Retrieved 11 March 2010. Any solid lighter than a fluid will, if placed in the fluid, be so far immersed that the weight of the solid will be equal to the weight of the fluid displaced.</span><span style="font-family: Calibri; font-size: 11.0000pt; mso-bidi-font-family: 'Times New Roman'; mso-fareast-font-family: SimSun; mso-spacerun: 'yes';"><o:p></o:p></span></div>
<div style="text-align: center;">
<span style="font-family: "times new roman" , serif; font-size: 12pt; text-align: center;"><br /></span></div>
<div align="center" class="MsoNormal" style="line-height: 150%; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: center;">
<span lang="EN-US" style="font-family: "times new roman" , serif; font-size: 12.0pt; line-height: 150%;"><o:p></o:p></span></div>
<br />
<div style="line-height: 150%;">
<br /></div>
<br />izzmirza mohsinhttp://www.blogger.com/profile/08473641161172340998noreply@blogger.comtag:blogger.com,1999:blog-411580745773753977.post-77722471224564175812018-05-07T09:52:00.002-07:002018-05-07T10:05:08.519-07:00BERNOULLI EQUATION<div class="MsoNormal">
<b><span style="font-family: "century gothic" , sans-serif; mso-bidi-font-family: "Times New Roman";">BERNOULLI
EQUATION<o:p></o:p></span></b></div>
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<b><span style="font-family: "century gothic" , sans-serif; mso-bidi-font-family: "Times New Roman";"><br /></span></b></div>
<div class="MsoNormal">
<b><span style="font-family: "century gothic" , sans-serif; mso-bidi-font-family: "Times New Roman";"><br /></span></b></div>
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhJqp6nTogUNXMyO89tX3h5uJQtMc1icIQKS_uIivQuTomfBrwo96wJ14TCnendT7O70j5DuZE5JM6YszbYc8IC_yGzJLd4YdXp3kIlzjuoCOD-HqxmuGZsaOWWF5rxkC8XmD299QZjaTLC/s1600/main-qimg-dccfc47fb45d022d875915c2b98cf951.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="401" data-original-width="589" height="217" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhJqp6nTogUNXMyO89tX3h5uJQtMc1icIQKS_uIivQuTomfBrwo96wJ14TCnendT7O70j5DuZE5JM6YszbYc8IC_yGzJLd4YdXp3kIlzjuoCOD-HqxmuGZsaOWWF5rxkC8XmD299QZjaTLC/s320/main-qimg-dccfc47fb45d022d875915c2b98cf951.png" width="320" /></a></div>
<div class="MsoNormal">
<b><span style="font-family: "century gothic" , sans-serif; mso-bidi-font-family: "Times New Roman";"><br /></span></b></div>
<div class="MsoNormal">
<b><span style="font-family: "century gothic" , sans-serif; mso-bidi-font-family: "Times New Roman";"><br /></span></b></div>
<div class="MsoNormal" style="line-height: 150%; text-align: justify;">
<span style="font-family: "century gothic" , sans-serif; mso-bidi-font-family: "Times New Roman";">An
approximate relation between pressure, velocity and elevation and valid in
regions of steady, incompressible flow where net frictional forces are
negligible. In simple way to understand, to know the relationship between
pressure and fluid velocity in the flow system.<o:p></o:p></span></div>
<div class="MsoNormal" style="line-height: 150%; text-align: justify;">
<span style="font-family: "century gothic" , sans-serif; mso-bidi-font-family: "Times New Roman";"><br /></span></div>
<div class="MsoNormal" style="line-height: 150%; text-align: justify;">
<span style="font-family: "century gothic" , sans-serif; mso-bidi-font-family: "Times New Roman";">Despite
its simplicity, it has been proven to be very powerful tool in fluids mechanics
which fluid motion is governed by the combined effects of pressure and gravity
forces. </span><span style="font-family: "century gothic" , sans-serif;">There
are 3 types main energy in the moving fluid which are:</span></div>
<div class="MsoListParagraph" style="line-height: 150%; mso-list: l0 level1 lfo1; text-align: justify; text-indent: -18.0pt;">
</div>
<ul>
<li>·<span style="font-size: 7pt; font-stretch: normal; font-variant-east-asian: normal; font-variant-numeric: normal; line-height: normal;"> </span><span style="font-family: "century gothic" , sans-serif; text-indent: -18pt;">Potential energy, energy which
possessed by fluid based on potential head (the height at point in fluid flow
measured from datum or reference line).</span></li>
</ul>
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<div align="center" class="MsoNormal" style="line-height: 150%; text-align: center;">
<span style="font-family: "century gothic" , sans-serif; mso-bidi-font-family: "Times New Roman";">P<sub>energy
</sub>= Z (m)<o:p></o:p></span></div>
<div class="MsoListParagraph" style="line-height: 150%; mso-list: l0 level1 lfo1; text-align: justify; text-indent: -18.0pt;">
</div>
<ul>
<li>·<span style="font-size: 7pt; font-stretch: normal; font-variant-east-asian: normal; font-variant-numeric: normal; line-height: normal;"> </span><span style="font-family: "century gothic" , sans-serif; text-indent: -18pt;">Kinetic energy, energy possessed by the
fluid particles based on it velocity.</span></li>
</ul>
<!--[if !supportLists]--><br />
<div align="center" class="MsoNormal" style="line-height: 150%; text-align: center;">
<span style="font-family: "century gothic" , sans-serif; mso-bidi-font-family: "Times New Roman";">K<sub>energy</sub>
= v <sup>2</sup> / 2g (m)<o:p></o:p></span></div>
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</div>
<ul>
<li>·<span style="font-size: 7pt; font-stretch: normal; font-variant-east-asian: normal; font-variant-numeric: normal; line-height: normal;"> </span><span style="font-family: "century gothic" , sans-serif; text-indent: -18pt;">Pressure energy, energy possessed by
fluid based on the pressure in the fluid.</span></li>
</ul>
<!--[if !supportLists]--><br />
<div align="center" class="MsoNormal" style="line-height: 150%; text-align: center;">
<span style="font-family: "century gothic" , sans-serif; mso-bidi-font-family: "Times New Roman";">P
= ρgh<o:p></o:p></span></div>
<div class="MsoNormal" style="line-height: 150%; text-align: justify;">
</div>
<div align="center" class="MsoNormal" style="line-height: 150%; text-align: center;">
<span style="font-family: "century gothic" , sans-serif; mso-bidi-font-family: "Times New Roman";">Therefore,
h = P / ρg<o:p></o:p></span></div>
<div align="center" class="MsoNormal" style="line-height: 150%; text-align: center;">
<span style="font-family: "century gothic" , sans-serif; mso-bidi-font-family: "Times New Roman";"><br /></span></div>
<div class="MsoNormal" style="line-height: 150%; text-align: center;">
<span style="font-family: "century gothic" , sans-serif; mso-bidi-font-family: "Times New Roman";"><br /></span></div>
<div class="MsoNormal" style="line-height: 150%; text-align: justify;">
<b><span style="font-family: "century gothic" , sans-serif; mso-bidi-font-family: "Times New Roman";">BERNOULLI THEOREM APPLICATION<o:p></o:p></span></b></div>
<div class="MsoNormal" style="line-height: 150%; text-align: justify;">
<b><span style="font-family: "century gothic" , sans-serif; mso-bidi-font-family: "Times New Roman";"><br /></span></b></div>
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</div>
<ul>
<li><span style="font-family: "century gothic" , sans-serif; text-indent: -18pt;"> Flow
through Uniform Pipe (meter, m)</span></li>
</ul>
<!--[if !supportLists]--><br />
<table border="1" cellpadding="0" cellspacing="0" class="MsoTableGrid" style="border-collapse: collapse; border: none; margin-left: 161.65pt; mso-border-alt: solid windowtext .5pt; mso-padding-alt: 0cm 5.4pt 0cm 5.4pt; mso-yfti-tbllook: 1184;">
<tbody>
<tr>
<td style="border: solid windowtext 1.0pt; mso-border-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 142.9pt;" valign="top" width="191"><div class="MsoNormal" style="line-height: 150%; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: justify;">
<span style="font-family: "century gothic" , sans-serif; font-size: 12.0pt; line-height: 150%;">H =P/ρg+
(v<sup>2</sup> )/2g+Z<o:p></o:p></span></div>
</td>
</tr>
</tbody></table>
<div class="MsoNormal" style="line-height: 150%; text-align: justify;">
<br /></div>
<div class="MsoListParagraphCxSpFirst" style="line-height: 150%; mso-list: l0 level1 lfo2; text-align: justify; text-indent: -18.0pt;">
</div>
<ul>
<li><span style="text-indent: -18pt;"> </span><span style="font-family: "century gothic" , sans-serif; text-indent: -18pt;">Flow
through Tapered Pipe</span></li>
</ul>
<!--[if !supportLists]--><br />
<div class="MsoListParagraphCxSpMiddle" style="line-height: 150%; mso-list: l1 level1 lfo1; text-align: justify; text-indent: -18.0pt;">
<!--[if !supportLists]--><span style="font-family: "symbol"; mso-bidi-font-family: Symbol; mso-fareast-font-family: Symbol;">·<span style="font-family: "times new roman"; font-size: 7pt; font-stretch: normal; line-height: normal;">
</span></span><!--[endif]--><span style="font-family: "century gothic" , sans-serif; mso-bidi-font-family: "Times New Roman";">The fluid flowing concept in a uniform
pipeline can be also used in a pipeline with different diameter.<o:p></o:p></span></div>
<div class="MsoListParagraphCxSpMiddle" style="line-height: 150%; mso-list: l1 level1 lfo1; text-align: justify; text-indent: -18.0pt;">
<span style="font-family: "century gothic" , sans-serif; mso-bidi-font-family: "Times New Roman";"><br /></span></div>
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</div>
<ul>
<li><span style="text-indent: -18pt;"> </span><span style="font-family: "century gothic" , sans-serif; text-indent: -18pt;">Flow
through Ventury Meter, (unitless)</span></li>
</ul>
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<span style="font-family: "century gothic" , sans-serif; mso-bidi-font-family: "Times New Roman";"><br /></span></div>
<div class="MsoNormal" style="line-height: 150%; text-align: justify;">
</div>
<div align="center">
<table border="1" cellpadding="0" cellspacing="0" class="MsoTableGrid" style="border-collapse: collapse; border: none; mso-border-alt: solid windowtext .5pt; mso-padding-alt: 0cm 5.4pt 0cm 5.4pt; mso-yfti-tbllook: 1184;">
<tbody>
<tr>
<td style="border: solid windowtext 1.0pt; mso-border-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 162.8pt;" valign="top" width="217"><div class="MsoListParagraphCxSpMiddle" style="line-height: 150%; margin-bottom: .0001pt; margin-bottom: 0cm; margin-left: 15.3pt; margin-right: 0cm; margin-top: 0cm; mso-add-space: auto; text-align: justify;">
<span style="font-family: "century gothic" , sans-serif; font-size: 12.0pt; line-height: 150%;">Q=A√(2gH/((m^2-1)))<o:p></o:p></span></div>
</td>
<td style="border-right: solid windowtext 1.0pt; border: none; mso-border-left-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 14.15pt;" valign="top" width="19"><div class="MsoListParagraphCxSpMiddle" style="line-height: 150%; margin-bottom: .0001pt; margin-bottom: 0cm; mso-add-space: auto; text-align: justify;">
<br /></div>
</td>
<td style="border-left: none; border: solid windowtext 1.0pt; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 184.65pt;" valign="top" width="246"><div class="MsoListParagraphCxSpLast" style="line-height: 150%; margin-bottom: .0001pt; margin-bottom: 0cm; margin-left: 16.25pt; margin-right: 0cm; margin-top: 0cm; mso-add-space: auto;">
<span style="font-family: "century gothic" , sans-serif; font-size: 12.0pt; line-height: 150%;">Q=Cd A√(2gH/((m^2-1)))<o:p></o:p></span></div>
</td>
</tr>
</tbody></table>
</div>
<div class="MsoNormal" style="line-height: 150%; text-align: justify;">
<b style="mso-bidi-font-weight: normal;"><span style="font-family: "century gothic" , sans-serif; mso-bidi-font-family: "Times New Roman";"><br /></span></b></div>
<div class="MsoNormal" style="line-height: 150%; text-align: justify;">
<b style="mso-bidi-font-weight: normal;"><span style="font-family: "century gothic" , sans-serif; mso-bidi-font-family: "Times New Roman";"><br /></span></b></div>
<div class="MsoNormal" style="line-height: 150%; text-align: justify;">
<b><span style="font-family: "century gothic" , sans-serif; mso-bidi-font-family: "Times New Roman";">CALCULATION</span></b></div>
<div class="MsoNormal" style="line-height: 150%; text-align: justify;">
<b style="mso-bidi-font-weight: normal;"><span style="font-family: "century gothic" , sans-serif; mso-bidi-font-family: "Times New Roman";"><br /></span></b></div>
<div class="MsoNormal" style="line-height: 150%; text-align: justify;">
<span style="font-family: "century gothic" , sans-serif;">1. </span><span style="font-family: "century gothic" , sans-serif; text-indent: -18pt;">Water
is flowing through a pipe with diameter of 150mm and 200mm at the bottom and
upper end respectively. The intensity of pressure at the bottom end is 200Pa
and the pressure at the upper end is 300Pa. Determine the difference in datum
head if the rate of flow through pipe is 0.05m</span><sup style="font-family: "Century Gothic", sans-serif; text-indent: -18pt;">3</sup><span style="font-family: "century gothic" , sans-serif; text-indent: -18pt;">/s.</span></div>
<div class="MsoNormal" style="line-height: 150%; text-align: justify;">
<br /></div>
<div class="MsoNormal" style="line-height: 150%; text-align: justify;">
<span style="font-family: "century gothic" , sans-serif; mso-bidi-font-family: "Times New Roman";"><b>Solution:</b><o:p></o:p></span></div>
<div class="MsoNormal" style="line-height: 150%; text-align: justify;">
<span style="font-family: "century gothic" , sans-serif; mso-bidi-font-family: "Times New Roman";"><b><br /></b></span></div>
<div class="MsoNormal" style="line-height: 150%; text-align: justify;">
<span style="font-family: "century gothic" , sans-serif; mso-bidi-font-family: "Times New Roman";">Given,
<o:p></o:p></span></div>
<div class="MsoNormal" style="line-height: 150%; text-align: justify;">
<span style="font-family: "century gothic" , sans-serif; mso-bidi-font-family: "Times New Roman";">Ø<sub>1</sub>
= 150mm = 0.15m, Ø<sub>2</sub> = 200mm = 0.2m, Q = 0.05 m<sup>3</sup>/s<o:p></o:p></span></div>
<div class="MsoNormal" style="line-height: 150%; text-align: justify;">
<span style="font-family: "century gothic" , sans-serif; mso-bidi-font-family: "Times New Roman";">P<sub>1</sub>
= 200Pa, P<sub>2</sub> = 300Pa, A = πd<sup>2</sup>/4<o:p></o:p></span></div>
<div class="MsoNormal" style="line-height: 150%; text-align: justify;">
<span style="font-family: "century gothic" , sans-serif; mso-bidi-font-family: "Times New Roman";"><br /></span></div>
<div class="MsoListParagraph" style="line-height: 150%; margin-left: 21.3pt; mso-add-space: auto; mso-list: l0 level1 lfo2; text-align: justify; text-indent: -18.0pt;">
<!--[if !supportLists]--><b style="mso-bidi-font-weight: normal;"><span style="font-family: "century gothic" , sans-serif; mso-bidi-font-family: "Century Gothic"; mso-fareast-font-family: "Century Gothic";"><span style="mso-list: Ignore;">a.<span style="font: 7.0pt "Times New Roman";">
</span></span></span></b><!--[endif]--><b style="mso-bidi-font-weight: normal;"><span style="font-family: "century gothic" , sans-serif; mso-bidi-font-family: "Times New Roman";">Find
each velocity,<o:p></o:p></span></b></div>
<div class="MsoListParagraph" style="line-height: 150%; margin-left: 21.3pt; mso-add-space: auto; mso-list: l0 level1 lfo2; text-align: justify; text-indent: -18.0pt;">
<b style="mso-bidi-font-weight: normal;"><span style="font-family: "century gothic" , sans-serif; mso-bidi-font-family: "Times New Roman";"><br /></span></b></div>
<div class="MsoNormal" style="line-height: 150%;">
<span style="font-family: "century gothic" , sans-serif; mso-bidi-font-family: "Times New Roman";"><span style="mso-tab-count: 3;"> </span>Q
= AV<o:p></o:p></span></div>
<div class="MsoNormal" style="line-height: 150%;">
<span style="font-family: "century gothic" , sans-serif; mso-bidi-font-family: "Times New Roman";"><br /></span></div>
<table border="0" cellpadding="0" cellspacing="0" class="MsoTableGrid" style="border-collapse: collapse; border: none; mso-border-insideh: none; mso-border-insidev: none; mso-padding-alt: 0cm 5.4pt 0cm 5.4pt; mso-yfti-tbllook: 1184;">
<tbody>
<tr style="height: 53.15pt; mso-yfti-firstrow: yes; mso-yfti-irow: 0; mso-yfti-lastrow: yes;">
<td style="height: 53.15pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 163.05pt;" valign="top" width="217"><div class="MsoNormal" style="line-height: 150%; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: justify;">
<span style="font-family: "century gothic" , sans-serif; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-fareast-theme-font: minor-fareast;">0.05 = (π </span><span lang="EN-US" style="font-family: "cambria math" , serif; mso-bidi-font-family: "Cambria Math"; mso-fareast-font-family: "Cambria Math";">〖</span><span style="font-family: "century gothic" , sans-serif; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-fareast-theme-font: minor-fareast;">(0.15)</span><span lang="EN-US" style="font-family: "cambria math" , serif; mso-bidi-font-family: "Cambria Math"; mso-fareast-font-family: "Cambria Math";">〗</span><span style="font-family: "century gothic" , sans-serif; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-fareast-theme-font: minor-fareast;">^2)/4 . v<sub>1</sub><o:p></o:p></span></div>
<div class="MsoNormal" style="line-height: 150%; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: justify;">
<span style="font-family: "century gothic" , sans-serif; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-fareast-theme-font: minor-fareast;">V<sub>1</sub> = 2.829 m<sup>2</sup>/s<o:p></o:p></span></div>
</td>
<td style="height: 53.15pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 148.8pt;" valign="top" width="198"><div class="MsoNormal" style="line-height: 150%; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: justify;">
<span style="font-family: "century gothic" , sans-serif; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-fareast-theme-font: minor-fareast;">0.05 = (π </span><span lang="EN-US" style="font-family: "cambria math" , serif; mso-bidi-font-family: "Cambria Math"; mso-fareast-font-family: "Cambria Math";">〖</span><span style="font-family: "century gothic" , sans-serif; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-fareast-theme-font: minor-fareast;">(0.2)</span><span lang="EN-US" style="font-family: "cambria math" , serif; mso-bidi-font-family: "Cambria Math"; mso-fareast-font-family: "Cambria Math";">〗</span><span style="font-family: "century gothic" , sans-serif; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-fareast-theme-font: minor-fareast;">^2)/4 .v<sub>2</sub><o:p></o:p></span></div>
<div class="MsoNormal" style="line-height: 150%; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: justify;">
<span style="font-family: "century gothic" , sans-serif; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-fareast-theme-font: minor-fareast;">V<sub>2</sub> = 1.59 m<sup>2</sup>/s<o:p></o:p></span></div>
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</tbody></table>
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<br /></div>
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<!--[if !supportLists]--><b style="mso-bidi-font-weight: normal;"><span style="font-family: "century gothic" , sans-serif; mso-bidi-font-family: "Century Gothic"; mso-fareast-font-family: "Century Gothic";"><span style="mso-list: Ignore;">b.<span style="font: 7.0pt "Times New Roman";">
</span></span></span></b><!--[endif]--><b style="mso-bidi-font-weight: normal;"><span style="font-family: "century gothic" , sans-serif; mso-bidi-font-family: "Times New Roman";">Use
Bernoulli Theorem, to find the difference in datum<o:p></o:p></span></b></div>
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<span style="font-family: "century gothic" , sans-serif; mso-bidi-font-family: "Times New Roman";">H = P/ρg+ (v<sup>2</sup>)/2g+Z<o:p></o:p></span></div>
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<span style="font-family: "century gothic" , sans-serif; mso-bidi-font-family: "Times New Roman";">P<sub>1</sub>/ρg+ </span><span lang="EN-US" style="font-family: "cambria math" , serif; mso-bidi-font-family: "Cambria Math"; mso-fareast-font-family: "Cambria Math";">〖</span><span style="font-family: "century gothic" , sans-serif; mso-bidi-font-family: "Times New Roman";">v<sub>1</sub></span><span lang="EN-US" style="font-family: "cambria math" , serif; mso-bidi-font-family: "Cambria Math"; mso-fareast-font-family: "Cambria Math";">〗</span><span style="font-family: "century gothic" , sans-serif; mso-bidi-font-family: "Times New Roman";">^2)/2g+Z<sub>1</sub>=P<sub>2</sub>/ρg+(</span><span lang="EN-US" style="font-family: "cambria math" , serif; mso-bidi-font-family: "Cambria Math"; mso-fareast-font-family: "Cambria Math";">〖</span><span style="font-family: "century gothic" , sans-serif; mso-bidi-font-family: "Times New Roman";">v<sub>2</sub></span><span lang="EN-US" style="font-family: "cambria math" , serif; mso-bidi-font-family: "Cambria Math"; mso-fareast-font-family: "Cambria Math";">〗</span><span style="font-family: "century gothic" , sans-serif; mso-bidi-font-family: "Times New Roman";">^2<span style="mso-spacerun: yes;"> </span>)/2g+Z<sub>2</sub><o:p></o:p></span></div>
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<span style="font-family: "century gothic" , sans-serif; mso-bidi-font-family: "Times New Roman";">200/9810 + (</span><span lang="EN-US" style="font-family: "cambria math" , serif; mso-bidi-font-family: "Cambria Math"; mso-fareast-font-family: "Cambria Math";">〖</span><span style="font-family: "century gothic" , sans-serif; mso-bidi-font-family: "Times New Roman";">(2.829)</span><span lang="EN-US" style="font-family: "cambria math" , serif; mso-bidi-font-family: "Cambria Math"; mso-fareast-font-family: "Cambria Math";">〗</span><span style="font-family: "century gothic" , sans-serif; mso-bidi-font-family: "Times New Roman";">^2<span style="mso-spacerun: yes;">
</span>)/(2(9.81))+Z<sub>1</sub>=300/9810+<span style="mso-spacerun: yes;">
</span>(</span><span lang="EN-US" style="font-family: "cambria math" , serif; mso-bidi-font-family: "Cambria Math"; mso-fareast-font-family: "Cambria Math";">〖</span><span style="font-family: "century gothic" , sans-serif; mso-bidi-font-family: "Times New Roman";">(1.59)</span><span lang="EN-US" style="font-family: "cambria math" , serif; mso-bidi-font-family: "Cambria Math"; mso-fareast-font-family: "Cambria Math";">〗</span><span style="font-family: "century gothic" , sans-serif; mso-bidi-font-family: "Times New Roman";">^2<span style="mso-spacerun: yes;"> </span>)/(2(9.81))+Z<sub>2<o:p></o:p></sub></span></div>
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<span style="font-family: "century gothic" , sans-serif; font-size: 12.0pt; line-height: 150%;">Z<sub>2</sub> - Z<sub>1</sub>=0.269 m</span></div>
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<span style="font-family: "century gothic" , sans-serif; font-size: 12.0pt; line-height: 150%;"><br /></span></div>
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<span style="font-family: "century gothic" , sans-serif; text-indent: -18pt;">2. </span><span style="font-family: "century gothic" , sans-serif; font-size: 12pt; text-indent: -18pt;">A sharp around the orifice of 50mm diameter water out of a tank. Column of water in the tank is 4.5m. find the coefficient of discharge if its discharged is 11.45 x 10</span><sup style="font-family: "Century Gothic", sans-serif; text-indent: -18pt;">-3 </sup><span style="font-family: "century gothic" , sans-serif; font-size: 12pt; text-indent: -18pt;">m</span><sup style="font-family: "Century Gothic", sans-serif; text-indent: -18pt;">3</sup><span style="font-family: "century gothic" , sans-serif; font-size: 12pt; text-indent: -18pt;">/s.</span></div>
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<b><span style="font-family: "century gothic" , sans-serif; font-size: 12pt; line-height: 24px;">S</span><span style="font-family: "century gothic" , sans-serif; font-size: 12pt;">olution:</span></b></div>
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<span style="font-family: "century gothic" , sans-serif; font-size: 12pt; line-height: 24px;">Q=Cd A√2gh<o:p></o:p></span></div>
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<span lang="EN-US" style="font-family: "cambria math" , serif; font-size: 12pt; line-height: 24px;">〖</span><span style="font-family: "century gothic" , sans-serif; font-size: 12pt; line-height: 24px;">11.45×10</span><span lang="EN-US" style="font-family: "cambria math" , serif; font-size: 12pt; line-height: 24px;">〗</span><span style="font-family: "century gothic" , sans-serif; font-size: 12pt; line-height: 24px;">^(-3)=Cd ( (π </span><span lang="EN-US" style="font-family: "cambria math" , serif; font-size: 12pt; line-height: 24px;">〖</span><span style="font-family: "century gothic" , sans-serif; font-size: 12pt; line-height: 24px;">(0.05)</span><span lang="EN-US" style="font-family: "cambria math" , serif; font-size: 12pt; line-height: 24px;">〗</span><span style="font-family: "century gothic" , sans-serif; font-size: 12pt; line-height: 24px;">^2)/4)√(2(9.81)(4.5))<o:p></o:p></span></div>
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<span style="font-family: "century gothic" , sans-serif; font-size: 12pt; line-height: 24px;">Cd=0.62</span></div>
izzmirza mohsinhttp://www.blogger.com/profile/08473641161172340998noreply@blogger.comtag:blogger.com,1999:blog-411580745773753977.post-4443249681054970032018-05-07T09:34:00.004-07:002018-05-07T10:05:38.018-07:00ARCHIMEDES' PRINCIPLE<h4 style="line-height: 150%;">
<span style="font-size: 11pt;"><b><span style="font-family: "verdana" , sans-serif;">What is Archimedes' Principle?</span></b></span></h4>
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<span style="font-family: "verdana" , sans-serif;"><span style="font-size: 11pt;">Archimedes' principle states that the upward buoyant force that is exerted on a body immersed in a fluid, whether fully or partially submerged, is equal to the weight of the fluid that the body displaces and acts in the upward direction at the center of mass of the displaced fluid. Archimedes' principle is a law of physics fundamental to fluid mechanics. It was formulated by Archimedes of Syracuse. </span><span style="font-size: 11pt;">Archimedes' principle does not consider the surface tension (capillarity) acting on the body. </span><span style="font-size: 11pt;">Moreover, Archimedes' principle has been found to break down in complex fluids</span><span style="font-size: 11pt;">.</span></span></div>
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<span style="font-family: "verdana" , sans-serif;"><span style="font-size: 11pt;">Fb = ρgV = ρghA</span><span style="font-size: 11pt;"><o:p></o:p></span></span></div>
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<span style="font-family: "verdana" , sans-serif;"><span style="font-size: 11pt;">Fb = buoyant force of a liquid acting on an object (N)</span><span style="font-size: 11pt;"><o:p></o:p></span></span></div>
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<span style="font-family: "verdana" , sans-serif;"><span style="font-size: 11pt;">ρ = density of the liquid(kg/m3)</span><span style="font-size: 11pt;"><o:p></o:p></span></span></div>
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<span style="font-family: "verdana" , sans-serif;"><span style="font-size: 11pt;">g = gravitational acceleration(9.80 m/s2)</span><span style="font-size: 11pt;"><o:p></o:p></span></span></div>
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<span style="font-family: "verdana" , sans-serif;"><span style="font-size: 11pt;">V = volume of liquid displaced (m3 or liters, where 1 m3 = 1000 L)</span><span style="font-size: 11pt;"><o:p></o:p></span></span></div>
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<span style="font-family: "verdana" , sans-serif;"><span style="font-size: 11pt;">h = height of water displaced by a floating object(m)</span><span style="font-size: 11pt;"><o:p></o:p></span></span></div>
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<span style="font-size: 11pt;"><span style="font-family: "verdana" , sans-serif;">A = surface area of a floating object(m2)</span></span><span style="font-family: "calibri"; font-size: 11.0000pt;"><o:p></o:p></span></div>
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<h3 style="line-height: 150%;">
<span style="font-family: "verdana" , sans-serif;"><span style="font-size: 11pt;"><b>Buoyancy Formula Questions:</b></span></span></h3>
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<!--[if !supportLists]--><span style="font-family: "verdana" , sans-serif;"><span style="font-size: 11pt;">1. </span><!--[endif]--><span style="font-size: 11pt;"> A golden crown has been placed in a tub of water. The volume of water displaced is measured to be 1.50 liters. The density of water is 1000 kg/m3, or 1.000 kg/L. What is the buoyant force acting on the crown?</span><span style="font-size: 11pt;"><o:p></o:p></span></span></div>
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<span style="font-family: "verdana" , sans-serif;"><span style="font-size: 11pt;"><b>Answer: </b></span></span></div>
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<span style="font-family: "verdana" , sans-serif;"><span style="font-size: 11pt;"><br /></span></span></div>
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<span style="font-family: "verdana" , sans-serif;"><span style="font-size: 11pt;">The buoyant force can be found using the formula. First, we ensure that the units used for volume are the same. If 1 m</span><span style="font-size: 11pt;">^</span><span style="font-size: 11pt;">3 = 1000 L, then 1.50 L = 0.00150 m</span><span style="font-size: 11pt;">^</span><span style="font-size: 11pt;">3. The buoyant force is:</span><span style="font-size: 11pt;"><o:p></o:p></span></span></div>
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<span style="font-family: "verdana" , sans-serif;"><span style="font-size: 11pt;">Fb = ρgV</span><span style="font-size: 11pt;"><o:p></o:p></span></span></div>
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<span style="font-family: "verdana" , sans-serif;"><span style="font-size: 11pt;">Fb = (1000 kg/m</span><span style="font-size: 11pt;">^</span><span style="font-size: 11pt;">3)(9.80 m/s2)(0.00150 m</span><span style="font-size: 11pt;">^</span><span style="font-size: 11pt;">3)</span><span style="font-size: 11pt;"><o:p></o:p></span></span></div>
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<span style="font-family: "verdana" , sans-serif;"><span style="font-size: 11pt;">Fb = 14.7 kg∙m/s</span><span style="font-size: 11pt;">^</span><span style="font-size: 11pt;">2</span><span style="font-size: 11pt;"><o:p></o:p></span></span></div>
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<span style="font-family: "verdana" , sans-serif;"><span style="font-size: 11pt;">Fb = 14.7 N</span><span style="font-size: 11pt;"><o:p></o:p></span></span></div>
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<span style="font-size: 11pt;"><span style="font-family: "verdana" , sans-serif;">The buoyant force acting on the golden crown is 14.7 N</span></span><span style="font-family: "calibri"; font-size: 11.0000pt;"><o:p></o:p></span></div>
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<h3 style="line-height: 150%;">
<span style="font-size: 11pt;"><span style="font-family: "verdana" , sans-serif;"><b>Explanation of Archimedes' P</b></span></span><b style="font-family: Verdana, sans-serif; font-size: 11pt;">rinciple by using picture</b></h3>
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izzmirza mohsinhttp://www.blogger.com/profile/08473641161172340998noreply@blogger.comtag:blogger.com,1999:blog-411580745773753977.post-12380726354912571522018-05-07T09:15:00.004-07:002018-05-07T09:15:39.849-07:00INTRODUCTION: BASIC EQUATION IN FLUID MECHANICS<br />
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<span style="font-size: 12pt; line-height: 150%;"><span style="font-family: Verdana, sans-serif;">Derivations of the basic equations of fluid mechanics are very
necessary because they fulfill the requirements for the broadest applicability
in areas of science and engineering. Fluid mechanics considerations are applied
in many fields, especially in engineering. Concerning the formulation of the
basic equations of fluids mechanics, it is easy to formulate the conservation
equations for mass, momentum, energy and chemical species for a fluid element.
The derivations of basic equations can be represented in an easily
comprehensible way and it is possible to build up the derivations upon the
basic knowledge of physics. Derivations of the basic equations are usually
followed by transformation considerations whose aim is to derive local
formulations of the conservation equations and to introduce field quantities into
the mathematical representations. <o:p></o:p></span></span></div>
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<span style="font-size: 12pt; line-height: 150%;"><span style="font-family: Verdana, sans-serif;"><br /></span></span></div>
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<span style="font-size: 12pt; line-height: 150%;"><span style="font-family: Verdana, sans-serif;"> The objective of
the derivations is to formulate the conservation laws for mass, momentum,
energy and chemical species in such a way that they can be applied to all the
flow problems that occur. Common equations in fluid mechanics are Bernoulli
equation. The equation is a statement of the conservation of energy in a form
useful for solving problems involving fluids. For non-viscous, incompressible
fluid in steady flow, the sum of pressure, potential and kinetic energies per
unit volume is constant at any point. Then, the common equation that used in
fluid mechanics are Navier-Stokes equations which are the motion of a non-
turbulent, Newtonian fluid is governed by that equation. The equation can be
used to model turbulent flow, where the fluid parameters are interpreted as
time-averaged values.in that case, there
are so many equations that have been derived to make a formula which can make
life easier in doing everyday works.</span><span style="font-family: Courier New, Courier, monospace;"><o:p></o:p></span></span></div>
<br />izzmirza mohsinhttp://www.blogger.com/profile/08473641161172340998noreply@blogger.com