Water Tunnel Experiment MAE 171A/175A. Objective:

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1 Wate Tunnel Expeiment MAE 7A/75A Objective: Measuement of te Dag Coefficient of a Cylinde Measuement Tecniques Pessue Distibution on Cylinde Dag fom Momentum Loss Measued in Wake it lase Dopple Velocimety - LDV

PA Revie of fluid motion Te motion of fluid depends on te Reynolds No.

2 Revie of Hydostatic Pessues Demonstation of pessue incease it dept Weigt of te column WmgAg Weigt is suppoted by te net pessue (P-P o )A P o A PP o g - Pessue inceases it dept - All points at a given dept ae at te same pessue PA Revie of fluid motion Te motion of fluid depends on te Reynolds No. - Lamina - Tubulent Te lamina flo may be pesented by steamlines Wen te fluid velocity is lage o en te fluid encountes most obstacles, te flo becomes tubulent

3 Descibing Fluid Beavio at Isotemal Conditions Consevation of Mass Netons Second La of Motion Consevation of Mass ( ) t i j k x y z - density - velocity t - time Constant density: Note: Tis is valid fo unsteady flo

4 Neton s Second La Eule s Equation F p t Dt D ) ( z g F F p pessue - body foce pe unit mass Assume body foce is due to gavity, and it is consevative g acceleation due to gavity Eule s Equation ) ( ) ( z g p t ) ( gz p t Vecto identity: Tus Constant density

5 Benoullis Equation Steady Rotational Flo ds gz p Conside Flo Along a Steamline Along a steamline const gz p Benoullis Equation Unsteady Iotational Flo φ gz p t φ const gz p t φ

6 Applications of Benoulli s Equation We Measue Flo Velocity Using Benoulli s Eqn: is detemined expeimentally Pitot tube as invented by a Fencman Heny Pitot in 73 Pessue Measuement Pocedue. Fo velocities of.8,.4, and.8 m/sec plot te pessue coefficient as a function of angle aound te cylinde on a single gap. Te pessue measuements ae located at te folloing angula positions Befoe te next lab meeting: Plot te pessue coefficient as a function of angle aound te cylinde on a single gap. Compae te measued pessue coefficient distibutions to tat fo te idealize flo aound te cylinde, C p -4 sin (θ), by plotting it along it te measued pessue coefficient.

7 Pat Dag fom Momentum Loss Measued in Wake it Lase Dopple Velocimety - LDV Lase Dopple Velocimety It is a poeful tecnique used fo igly accuate measuement of fluid velocity in liquid o gaseous flo It as developed in 964 by Ye and Cummins to measue lamina ate flo Does not distub te fluid flo Te tecnique as been impoved ove te yeas and it as vaiety of applications

8 Ho does it ok? Intensity stat of finge patten end Diection alo Flo A pai of lase beams ae focused don to ceate intefeence finges at te optical volume fomed Due to te Gaussian intensity distibution of te lase beam, te finges at te cente of te focal volume ill be bigte Pat Dag fom Momentum Loss Measued in Wake it Pessue Aay

9 Dag Coefficient u A B u u A B u(y) y x incompessible Dag Coefficient Mass Consevation Coss Section: (Rate of Flo) AB AA b u BB b A B b dy bu udy ( u u) dy

10 Dag Coefficient Equation of Motion steady Flo: ( p dv [ ) ] Dag Reynolds Tanspot Teoem FdV F nda pnda Dag Dag nda If static pessue on AA, BB ae same nda Equation of Motion Coss Section AB AA BB A B Dag Coefficient Dag nda bu b b u u dy ( u u) dy b u( u u) dy u u u bu u dy

11 Dag on Cylinde: Pe unit lengt (b ) Dag Coefficient Dag u u u bu u dy Te Dag Coefficient C D Tis is measued using Pitot tube

12 Velocity Measuement Pocedue Velocity Measuement Pocedue

13 Tapezoidal Rule Diect ay to calculate numeical integal is by beaking of te aea unde te cuve into small knon aea squaes and counting te squaes Anote ay is to beakup te cuve into staigt line segments, teefoe ceating tapezoids and add up te aeas of tese geometic figues Te aea of a single tapezoid (it idt and eigt a and b) Aea(ab)/ a b Tapezoidal Rule Apply tis ule to an integal I: b a I f ( x) dx Appoximate I it a finite diffeence: I N i i i i i [ f ( x ) f ( x )]( x x ) Hee i is an index tat goes fom te fist data point (i) up to last data point available, in, x i is te value of te independent vaiable at te i-t datapoint, and f(x i ) is value of te function f at x i.

14 Refeences. Jon D. Andeson, Fundamentals of Aeodynamics, nd Ed., pp. 95- and pp. 8-36, McGa Hill 99.. L. E. Dain, Te Lase Dopple Tecnique, Jon Wiley & Sons Hais Benson, Univesity Pysics, Capte 4, Jon Wiley & Sons ttp://clients.dedicatedconsulting.com/aeometics/ldv.tml#ldv Effect of Finite Viscosity Wat is te Reynolds numbe? Te Reynolds numbe is te atio of inetial foces, as descibed by Neton's second la of motion, to viscous foces

Wind Tunnel Experiment MAE 171A/175A. Objective:

Wind Tunnel Experiment MAE 171A/175A. Objective: Wind Tunnel Exeiment MAE 7A/75A Objective: Measue te Aeodynamic Foces and Moments of a Clak Y-4 Aifoil Unde Subsonic Flo Conditions Measuement Tecniques Pessue Distibution on Aifoil Dag fom Momentum Loss