|
|
| Line 1: |
Line 1: |
| The '''pressure coefficient''' is a [[dimensionless number]] which describes the relative pressures throughout a flow field in [[fluid dynamics]]. The pressure coefficient is used in [[aerodynamics]] and [[hydrodynamics]]. Every point in a fluid flow field has its own unique pressure coefficient, <math>C_p</math>.
| | I woke up last week and noticed - luke bryan tickets for sale [[http://www.cinemaudiosociety.org http://www.cinemaudiosociety.org]] I have been solitary for a little while at the moment and after much bullying from buddies I today locate myself signed up for on line dating. They promised me that there are plenty of pleasant, standard and interesting individuals to fulfill, so here goes the toss!<br>I strive to keep as physically healthy as [http://www.Google.de/search?q=potential potential] staying at the gym several-times a week. I love my athletics and try to play or watch as numerous a potential. Being winter I'll regularly at Hawthorn matches. Notice: I've observed the carnage of fumbling suits at stocktake sales, If you contemplated shopping a sport I do not mind.<br>My pals and household are awe-inspiring and spending time together at pub gigabytes or dishes is obviously a necessity. I have never been into night clubs as I realize that one may do not get a decent dialog with the [http://lukebryantickets.hamedanshahr.com Tickets To Luke Bryan] noise. I additionally have two undoubtedly cheeky and quite adorable canines that are almost always eager to meet new folks.<br><br>Stop by my homepage ... [http://lukebryantickets.omarfoundation.org front row tickets] |
| | |
| In many situations in aerodynamics and hydrodynamics, the pressure coefficient at a point near a body is independent of body size. Consequently an engineering model can be tested in a [[wind tunnel]] or [[water tunnel (hydrodynamic)|water tunnel]], pressure coefficients can be determined at critical locations around the model, and these pressure coefficients can be used with confidence to predict the fluid pressure at those critical locations around a full-size aircraft or boat.
| |
| | |
| ==Incompressible flow==
| |
| The pressure coefficient is a parameter for studying the flow of incompressible fluids such as water, and also the low-speed flow of compressible fluids such as air. The relationship between the dimensionless coefficient and the dimensional numbers is
| |
| <ref>Clancy, L.J., ''Aerodynamics'', section 3.6</ref> | |
| <ref>Abbott and Von Doenhoff, ''Theory of Wing Sections'', equation 2.24</ref>
| |
| | |
| :<math>C_p = {p - p_\infty \over \frac{1}{2} \rho_\infty V_{\infty}^2 }</math>
| |
| where:
| |
| : <math>p</math> is the [[Static pressure#Static pressure in fluid dynamics|pressure]] at the point at which pressure coefficient is being evaluated
| |
| : <math>p_\infty</math> is the pressure in the [[freestream]] (i.e. remote from any disturbance)
| |
| : <math>\rho_\infty</math> is the freestream [[density|fluid density]] (Air at [[sea level]] and 15 °C is 1.225 <math>kg/m^3</math>)
| |
| : <math>V_\infty</math> is the freestream velocity of the fluid, or the velocity of the body through the fluid
| |
| | |
| Using [[Bernoulli's Equation]], the pressure coefficient can be further simplified for incompressible, lossless, and steady flow:<ref>Anderson, John D. ''Fundamentals of Aerodynamics''. 4th ed. New York: McGraw Hill, 2007. 219.</ref>
| |
| | |
| :<math>C_p ={1 - \bigg(\frac{V}{V_{\infty}} \bigg)^2}</math>
| |
| | |
| where V is the velocity of the fluid at the point at which pressure coefficient is being evaluated.
| |
| | |
| This relationship is also valid for the flow of compressible fluids where variations in speed and pressure are sufficiently small that variations in fluid density can be ignored. This is a reasonable assumption when the [[Mach Number]] is less than about 0.3.
| |
| | |
| * <math>C_p</math> of zero indicates the pressure is the same as the free stream pressure.
| |
| * <math>C_p</math> of one indicates the pressure is [[stagnation pressure]] and the point is a [[stagnation point]].
| |
| * <math>C_p</math> of minus one is significant in the design of [[Glider (sailplane)|gliders]] because this indicates a perfect location for a "Total energy" port for supply of signal pressure to the [[Variometer]], a special Vertical Speed Indicator which reacts to vertical movements of the atmosphere but does not react to vertical maneuvering of the glider.
| |
| | |
| In the fluid flow field around a body there will be points having positive pressure coefficients up to one, and negative pressure coefficients including coefficients less than minus one, but nowhere will the coefficient exceed plus one because the highest pressure that can be achieved is the [[stagnation pressure]]. The only time the coefficient will exceed plus one is when advanced boundary layer control techniques, such as blowing, is used.
| |
| | |
| ==Compressible flow==
| |
| In the flow of compressible fluids such as air, and particularly the high-speed flow of compressible fluids, <math>{\rho v^2}/2</math> (the [[dynamic pressure]]) is no longer an accurate measure of the difference between [[stagnation pressure]] and [[static pressure]]. Also, the familiar relationship that [[stagnation pressure]] is equal to ''total pressure'' does not always hold true. (It is always true in [[Isentropic process|isentropic]] flow but the presence of [[shock wave]]s can cause the flow to depart from isentropic.) As a result, pressure coefficients can be greater than one in compressible flow.<ref>http://thesis.library.caltech.edu/608/1/Scherer_lr_1950.pdf</ref>
| |
| | |
| * <math>C_p</math> greater than one indicates the freestream flow is compressible.
| |
| | |
| == Pressure distribution ==
| |
| An airfoil at a given [[angle of attack]] will have what is called a pressure distribution. This pressure distribution is simply the pressure at all points around an airfoil. Typically, graphs of these distributions are drawn so that negative numbers are higher on the graph, as the <math>C_p</math> for the upper surface of the airfoil will usually be farther below zero and will hence be the top line on the graph.
| |
| | |
| == <math>C_l</math> and <math>C_p</math> relationship ==
| |
| The [[coefficient of lift]] for an airfoil with '''strictly horizontal surfaces''' can be calculated from the coefficient of pressure distribution by integration, or calculating the area between the lines on the distribution. This expression is not suitable for direct numeric integration using the panel method of lift approximation, as it does not take into account the direction of pressure-induced lift.
| |
| | |
| :<math>C_l=\int\limits_{LE}^{TE}\left(C_{p_l}(x)-C_{p_u}(x)\right)\,d \frac{x}{c}</math> | |
| | |
| where:
| |
| | |
| :<math>C_{p_l}</math> is pressure coefficient on the lower surface
| |
| :<math>C_{p_u}</math> is pressure coefficient on the upper surface
| |
| :<math>LE</math> is the leading edge
| |
| :<math>TE</math> is the trailing edge
| |
| | |
| When the lower surface <math>C_p</math> is higher (more negative) on the distribution it counts as a negative area as this will be producing down force rather than lift.
| |
| | |
| == See also ==
| |
| * [[Lift coefficient]]
| |
| * [[Drag coefficient]]
| |
| * [[Pitching moment#Coefficient|Pitching moment coefficient]]
| |
| | |
| ==References==
| |
| * Clancy, L.J. (1975) ''Aerodynamics'', Pitman Publishing Limited, London. ISBN 0-273-01120-0
| |
| * Abbott, I.H. and Von Doenhoff, A.E. (1959) ''Theory of Wing Sections'', Dover Publications, Inc. New York, Standard Book No. 486-60586-8
| |
| * Anderson, John D (2001) ''Fundamentals of Aerodynamic 3rd Edition'', McGraw-Hill. ISBN 0-07-237335-0
| |
| | |
| {{reflist}}
| |
| | |
| [[Category:Aerospace engineering]]
| |
| [[Category:Dimensionless numbers of fluid mechanics]]
| |
| [[Category:Fluid dynamics]]
| |
I woke up last week and noticed - luke bryan tickets for sale [http://www.cinemaudiosociety.org] I have been solitary for a little while at the moment and after much bullying from buddies I today locate myself signed up for on line dating. They promised me that there are plenty of pleasant, standard and interesting individuals to fulfill, so here goes the toss!
I strive to keep as physically healthy as potential staying at the gym several-times a week. I love my athletics and try to play or watch as numerous a potential. Being winter I'll regularly at Hawthorn matches. Notice: I've observed the carnage of fumbling suits at stocktake sales, If you contemplated shopping a sport I do not mind.
My pals and household are awe-inspiring and spending time together at pub gigabytes or dishes is obviously a necessity. I have never been into night clubs as I realize that one may do not get a decent dialog with the Tickets To Luke Bryan noise. I additionally have two undoubtedly cheeky and quite adorable canines that are almost always eager to meet new folks.
Stop by my homepage ... front row tickets