Symbolic circuit analysis: Difference between revisions

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{{refimprove|date=December 2012}}
In a [[nozzle]] or other constriction, the '''discharge coefficient''' (also known as '''coefficient of discharge''') is the ratio of the actual discharge to the theoretical discharge,<ref>Sam Mannan, Frank P. Lee, ''Lee's Loss Prevention in the Process Industries: Hazard Identification, Assessment and Control'', Volume 1, Elsevier Butterworth Heinemann, 2005. ISBN 978-0750678575. [http://books.google.ca/books?id=UDAwZQO8ZGUC&pg=SA15-PA7&lpg=SA15-PA7&dq=define:coefficient+of+discharge&source=bl&ots=2mXq9FXJUT&sig=x_YGCLqbpRbmPNy9iwSUvXjDhRs&hl=en&sa=X&ei=XcUqUIqPJeeO6gHJ8oDoBw&redir_esc=y#v=onepage&q=define%3Acoefficient%20of%20discharge&f=false (Google books)]</ref> i.e., the ratio of the [[mass flow rate]] at the discharge end of the [[nozzle]] to that of an ideal nozzle which expands an identical [[working fluid]] from the same initial conditions to the same exit pressures.<br/>
<br/>
Mathematically the discharge coefficient may be related to the mass flow rate of a fluid through a straight tube of constant cross-sectional area through the following equation:<ref>Frank M. White, ''Fluid Mechanics, 7th Edition''</ref><ref>http://www.isa.org/books/Mulley_Papers/compressible.html</ref>


<math>C_d A = \dfrac{\dot{m}}{\sqrt{{2}{g_c}{\rho}{\Delta} {P}}}</math>


Where:<br/>
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<math>C_d</math> = Discharge Coefficient through the constriction (unit-less).<br/>
<math>A</math> = Cross-sectional area of flow constriction (unit length squared).<br/>
<math>\dot{m}</math> = Mass flow rate of fluid through constriction (unit mass of fluid per unit time).<br/>
<math>{g_c}</math> = Gravitational constant (Dimensionless)<br/>
<math>\rho</math> = Density of fluid (unit mass per unit volume).<br/>
<math>\Delta P</math> = Pressure drop across constriction (unit force per unit area).<br/>
<br/>
This parameter is useful for determining the irrecoverable losses associated with a certain piece of equipment (constriction) in a fluid system, or the "resistance" that piece of equipment imposes upon the flow.
 
This flow resistance, often expressed as a unit-less parameter, <math>k</math>, is related to the discharge coefficient through the equation:
 
<math>k = \dfrac{1}{C_d^{2}}</math>
 
which may be obtained by substituting <math>\Delta P</math> in the aforementioned equation with the resistance, <math>k</math>, multiplied by the [[dynamic pressure]] of the fluid, <math>q</math>.
 
== See also ==
* [[Flow coefficient]]
* [[Orifice plate]]
 
==References==
{{reflist}}
 
==External links ==
* [http://mysite.du.edu/~jcalvert/tech/fluids/orifice.htm Coefficient of Discharge], J. B. Calvert, 15 June 2003
 
[[Category:Fluid dynamics]]
 
 
{{fluiddynamics-stub}}

Latest revision as of 15:25, 2 January 2015


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