Introduction to Fluid Mechanic
Introduction to Fluid Mechanic CE 321
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This 42 page Class Notes was uploaded by Jolie Shields on Saturday September 19, 2015. The Class Notes belongs to CE 321 at Michigan State University taught by Roger Wallace in Fall. Since its upload, it has received 39 views. For similar materials see /class/207369/ce-321-michigan-state-university in Civil Engineering at Michigan State University.
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Date Created: 09/19/15
CE321 Fluid Mechanics Fall 2009 Friday September 4 2009 Lecture 2 Fluid Properties Fluid Mechanics Fluid mechanics is concerned with the study of fluids liquids and gases at rest or in motion Examples Flow of blood in the arteries Flow past an aircraft Flow called circulation in Lake Michigan Flow through a pipe Q What is the difference between fluids and soHds Fluids as a class of matter are distinguished from solids on the basis of their response to an applied shear stress A solid distorts to attain an equilibrium displacement to balance the applied force A fluid can not be under equilibrium under the action of an external force it continues to flow Some fluids have complex behavior Units amp Dimensions Qualitative and quantitative WW ipw s Qualitative Length Time Stress etc Quantitative Numerical measure Units are standards eg kg for mass Primary quantities L M T Secondary quantities derived from Dimensional Homogeneity The left and right hand side o a equation should have the same units All the individual telms In an equation regardless of which side should have the same units System of Units at ritieh Gravitational 86 Foot length second time slug mass pound lb for force and 0F for temperature 1 lb 1 slug x 1 le How much does a mass of 1 slug weigh W mg W lb 1 slug x 322 le2 322 lb System of Units SI Internativu System Meter length second time kg mass and Newton force 1 N 1 kg x 1 ms2 Unit of work is the Joule 1 J 1 Nm Unit of power is Watt 1 W 1 Js 1 Nms Fluid Mechanics Fluid Statiw Deals with luids at rest Fluid Dynamics Fluids in motion Properties of Fluids Density Specific Weight Specific Gravity Bulk Modulus Vapor Pressure Viscosity Surface Tension Density p Defined as mas per unit volume p mV Units kgm3 or slugft3 Varies widely for different fluids Ior quwds l and I usually nave a small effect on density specmc vclume IS tne velume per unit mass and is the reciprocal of density Density as a function of T Specific Weight y VVVIuI IL IO VIII Ivd MU tl IV vvviul IL per unit volume V 99 Units Nm3 or Ibft3 Used to characterize the weight of a s stem 4 y quotn 0957 w a 9 M gter Q t 9 239 3 Specific Gravity SG Is the ratio of the density of the fluid to 0 the density of water at some specified 0 0 temperature usually H204 C 40 C Units What is Pressure Normal force per unit area Nm2 Absolute Pressure Relative Pressure Ideal Gas Law for gases highly compressible also called the equation of state Units of pressure lbin2 psi or Nm2 Pa p in the above equation is the absolute pressure ie relative to the pressure in a perfect vacuum which is zero T is the absolute temperature K or R R Universal gas constant from tables Gage Pressure Standard atmospheric pressure a cw level is 147 psi abs or 101 kPa abs If pressure is measured relative to me local atmospheric pressure it is called gage pressure Abs P Gage P Atm P Viscosity u This property characterizes the ease which a fluid flows the fluidity of the fluid Viscosity is a measure of the resistance that a fluid offers to applied shear forces This resistance does not depend on the deformation itself as it does for solids but on the rate of deformation I gt I u u yu y gt I A 5B Frxcd male r Read Section 16 in your textbook Viscosity u u is called the dynamic viscos Plots of shear stress 1 as a function of dudy should be linear with slope equal to the viscosity Viscosity is different for different fluids why and is a function of temperature why u dynamic Units FTL392 Nsm2 lbsft2 Slmari g stress 139 CHHUQ 013 60 39F Mater BIL Ht Water 1 mu M Air 60 F 7 a Hate Of Weaning strain E Newtonian Fluids Fluids for which the shear guess 9 wan related to the rate of shear strain are called Newtonian uds Most common fluids are Newtonian Examples of nonNewtonian fluids egg yolk silly putty honey M My Kinematic Viscosity v Is the ratio of dynamic viscosity to the dens y Units m2s V g p Bulk Modulus Is a measure of how easily the volume and E dp hence the density of a dVV fluid changes due to m pV changes in pressure d d Units FL2 9 Wm2 E p e 1 LargeE dVV Clip0 lncompressible fluid For common liquids E values are large as expected Compression and Expansion of Gases As gases are expanded or compressed the relation between P and density de ends on the nature of the rocess Isothermal process T constant p p constant Isentropic process no heat exchange p pk constant k ratio of specific heats k p C Speed of Sound A consequence of the dp compressibility of C E fluids d Air is more P compressible than dPp water C E Disturbances travel at p a finite veIOCIty E kp Surface Tension The cohesive forces between molecules down into a liquid are shared with all neighboring atoms Those on the surface have no neighboring atoms above and exhibit stron39er attractive forces upon their nearest neighbors on the surface This enhancement ofthe intermolecular attractive forces at the surface is called surface tension Adhesion and Cohesion Attraction between m moowes s WNW adhesion Attraction between dissimilar molecules is cohesion Surface Tension o a it Ci Cohesion gt Adhesion Adhesion gt Cohesion Problem 15 The volume rate of flow Q through a pipe containing a slowlymoving liquid is given by the equation Q 7Z39R4Ap 8y where R is the pipe radius A the pressure drop along the pipe a a fluid property called viscosity andE the length of the pipe What are the dimensions of the constant 7r8 Would you classify this equation as a genera vvew equuwn p Problem 15 Solution 7rR4Ap W M J 3 1 LY FLal L T LE wimp PTJ 41 m The Canskan t 178 142 uv lan a general homogeneous eZLuJ l39Dn 1114A is Vah39d H mm CansfsJen39f MnH 5554 V35 ls dimensw ess Amt 13 113 The density 0139 21 certain liquid is 215 slugsI5 Deter 39 39 I a mint its speci c weight and speci c gravity gem 15 izz 472 53 z r 75 1g 567 0 W m H 7 Lg 119 Some experiments are being conducted in a labo ramry in which the air temperature is 27 C and he auno spheric pressure is 143 psia Determine the density of the 1 air Express your answers in slugsfl3 and In k m 7bpi T 7 mmel wa 2739 L l aza 9F 39 30quot 6F 39 1 i 315 7 M mm aye slur slurp ft 3 dsz 71 000222 25 slug 0 oaoa222 Fa54X m 7 43 and a kinemaric viscosi f m ls lows past a xed surface Due to the noslip condition the velocity at the xed surface is zero as shown in Video V12 and he velncity pm le near the surface is shown in Fig H28 De cmAim m magnitu e and direclion of the shearing stress developed on the plate Express your answer in terms of U and 6 with U and 5 expressed in unlrs of mekersvper sec r and and meters respectlve y 128 A Newtonian fluid having a speci c gravity of 092 ly o 4 X r quot 7 l I LU 2 51044 5 9 4 45 i0 128 Solution 5 d z 392 da 39 J J Shut 7 Tsum ze W 2 3 U im g Mzm J ami W M 7L0 M 4quot PM uo When a viscous uid flows past a Ihin sharpedged plain a hill layer adjacent in the plate surface develops in which rhe veiociry u changes rapidly from zero to a a 39n 3 sm 339 the disranee x along rhe plate as shown in r i 3 sumc r a 14 U and s SiSVVxU kinemsric viscosiry of rhe uid Determine an expression for rhe fume drag rhnr would be dcvcluped on one side arrhe piare of iengrh I and width b Expioss your answer in renns o b v and p where p is me uid dcnsitv i IJU Burnhmw inyar 130 Solution Drag agf 71 14 Unu 14 Adx Jo u l Ogf72rtdx x U 0 I in a SIM 7 la 0 and a A bi J 55 I 39 A an 149m Eglfl J1 54 quotg i If D X Dz Z 399 D ifVVZ lax 51114 0 dx 771 L I 145 n9 427115 214 5 3 MA w h 7 19 057AFV11y3 136 The viscosity of a soft drink was determined by using a capillary tube viscometer similar to that shown in Fig P136 and Video V13 For this device the kinematic viscosity v is directly proportional to the time I that it takes for a given amount of liquid to ow through a small capil lary tube That is v Kt The following data were obtained from regular pop and diet pop The corresponding measured speci c gravities are also given Based on these data by what percent is the absolute viscosity u of regular pop greater than that of diet pop Diet pop 3003 Regular pop 3778 Glass strengthening bridge Capillary tube it L 136 solution A7W49r Z100 g Jile dfet V39cm Sbce quot39VzJOJ 7 kix lm j39oyzapyoc ff v pws 77m v gt 0 Wafer 0 r63 ljx mo 140 M a t w 56 Jx loo fx swam 30035I003 37780W J x top 30 There are many fluids lhat cxliibii nunNewtonian 11 gt For given nuiu Iliamum an m uxmn c View v14 he dislinctinn belween Newtonian and nonNewtonian be havior is usually based on measurements 0 ear stress and 39 um 1 God is to be determined by measu 5 ea me of shearing strain dudy chlaincd from a small 1 sample tested in a suitable viscomclcr sad given below delerminc if the blond is a Newtonian or non Newtonian uid Explain lmw you arrived at your answer 1Nsz 004 006 012 7 030 052 Hz 2 10 nilmiquot 125 450 1125 225 450 900 225 450 a a I J39J 139 solution For a MenLam Ha394 7397quot ratn 12 2 1 3 4245 15 a 4mg 5 171 JILL ydtrrf IVSm manta 9 0957 10175 0 M73 Idai 0 097 i Juy 0 9050 may 7 ma a 1 not a ansmi buquot durum v5 le m 057901 tnm Mcmxes Thy 7773 fm39z HM x a mIVta oan fluid 4 nat m 7 11 mu 3 sham Avgow Fur IanAw 7nd 771 darn wand 5 n SfI IIjIt ling M77 4 slap f o 739 MW mg gI Ei i asii39u iaaaa n II III Shear Stress vs Rate of Shearing Strain IJU solution 9 EEE39 Expe mental Data Gill S1upe 11 Vera Newtoman Hum III II 10 100 10m dudy 5M 132 A 40lb O8 ftdiameler lft tall cylindrical tank slides slowly down a ramp with a constant speed of 01 NS as shown in Fig P132 The uniformltthickness oil layer on the ramp has a viscosity of 02 lb sftz Determine the an gle 9 of the ramp Tank 0002 ft
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