FM Lecture Notes 9.ppt

7/23/2019 FM Lecture Notes 9.ppt

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CHAPTER 8

ADDITIONAL SUBJECTS IN

FUNDMENTALS OF FLOW

Dr . Ercan Kahya


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Vorticityfor the z axis:

When vorticity is zero,

irrotational lo!


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Case (a): rotational flow

Case (b): irrotational flow Although liquid maes a rotary movement, its microelements

always face the same direction without !erforming rotation"

#n natural vortices such as hurricanes, tornados, eddying water currents has a

basic structure with a forced vortex at thecenter and free vortex at the !eri!hery"

$igure shows howthe wood chi!s float


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%iven closed curve s, the integrated vs& along this same curve is

called circulation ' " aing counterclocwise rotation !ositive,


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Circulation d' of elemantary rectangle AC* (area dA)

+ the circulation is equal to the !roduct of vorticity by area" #ntegration gives

toes theorem: surface integral of vorticity equal to the circulation

#f there is no vorticity inside a closed curve, then circulation around it is zero"


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Flo! o "i#co$# l$i%

-ass flow rate at inlet + outlet sections in x. + y.directions


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$luid mass stored in the fluid element !er unit time (x.dir") :

$luid mass stored in the fluid element !er unit time (y.dir") :

-ass change in unit time (right hand side) :

or

Continuity /quation0nsteady flow + com!ressible fluid

+ for real and ideal fluid


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$or steady flow and incom!ressible fluid:

$or steady flow and incom!ressible fluid for axially

symetric flow using cylindrical coordinates:


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$or axially symetric flow using cylindrical coordinates:


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he strict solutions obtained for 1. equations to date are

only for some s!ecial flows" wo such exam!les are:

$low of a viscous fluid between two !arallel !lates


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A flow in a long circular !i!e is a !arallel flow of axial symmetry"#n this case, it is convenient to use the 1avier.toes equation using

cylindrical coordinates

0nder the same conditions as in the !revious section, 1.

equation sim!lifies to

FM Lecture Notes 9.ppt

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