EME 303 - FLUID MECHANICS SUMMARIZED EQUATIONS AND CONCEPTS

Some Useful Conversion Factors

SI BGS EE Temperature: 273 15oK C= + . 459 67o oR F= + . 459 67o oR F= + . Force: 21 (1 )(1 )N kg m s= / 21 (1 )(1 )lb slug ft s= / 21 (1 )(32 2 )lbf lbm ft s= . / Mass: kg slug lbm Density: 31kg m/ 30.00194 slug ft/ 30.06243 lbm ft/

water! 31000kg m/ 31 94slugs ft. / 362 4lbm ft. / Pressure: 21 1Pa N m= / 20.0209 lb ft/ 20.0209 lbf ft/ Work, energy: 1 1J N m= . 1 778 2ft lb Btu. = . — Power: 1 1W N m s= . / 1 550hp ft lb s= . / —

General [Topic:1]

or x x

y y

z z

F am F m a

F a

! " ! "# # # ## # # ## # # #$ % $ %# # # ## # # ## # # #& ' & '

= =F a

k

pIsothermal const

p RTp

Isentropic const

!!

!

" : = .##= $# : = .#%

;dudy

µ! µ "#

= =

vdpE

d V= !

V/dp

d" "=

/

2 cosh

R! "#

=

!

EME 303 Fluid Mechanics 33!© 2013 Derek Elsworth

[1:3] Fluid Properties

Recap Definitions Dimensional homogeneity Fluid properties Mass and Weight Equations of State Compressibility

Outline Wave Speeds Viscosity Vapor pressure (airfoil) Surface tension (vinometer)

Topic 2 Pressure Fluid pressure at a point

Incompressible (water) Compressible (atmosphere)

p = ρRT M = ρV ;W = Mg

Ev = −

dpdV / V0

= +dp

dρ / ρ0

τ = µ ∂vx

∂y

http://en.wikipedia.org/wiki/Supercritical_fluid

c = gy or Ev / ρhttp://www.youtube.com/watch?v=629em0mPpUY

Fluid Statics [2,3] x y zp p p p= = =

0ˆ or 0

1

x

y

z

x ap p a

ya

z

! " ! "

# $% %% %% %& '% %% %% %( )

# $*% %*% % # $*% % % %+, + = + + =& ' & '*% % % %( )% %*

% %*( )

k a

Simplifies when: 0 to 0 and ; xy

zx z

adp dp dp dza a a

dx dy dz dx g a!= = = = = = " = "

+

2

2 2

22

2

Rigid body rotation: 0 ;p r

rgz cp p pr

r z p z c

!

!" ! #

#$

% = +& & & '=+

; = ; = ( )& & & = ('*

0Incompressible fluid: p h p!= +

Compressible fluid: and integrate w.r.t ( )dp gp p zdz RT

= ! , .

Manometer rules: ( )( ) 0 if evacuated; 0v gasdp dp

ve ve pdx dy

!" # $ + ; = = ; % .

2 2

R c R H VF h A F F F!= ; = +

acts through center of pressure

xcR c

cR

xycR c

c

Iy y

y AF

Ix x

y A

!""""#""""$

= +

= +

BF V!=

!

EME 303 Fluid Mechanics 71!© 2013 Derek Elsworth

[2:2] Fluid Statics

Recap Fluid pressure at a point (static)

Incompressible (water) Compressible (atmosphere)

Outline Pressure measurement (manometry)

px = py = pz = p

!"p !# k̂ = $a or !

%%x%%y%%z

&

'

(((

)

(((

*

+

(((

,

(((

p !#001

&'(

)(

*+(

,(= $

ax

ay

az

&

'

(((

)

(((

*

+

(((

,

(((

Simplifies when: ax = ay = az = 0 to

dpdx

= dpdy

= 0 and dpdz

= !"

Incompressible fluid: p = ! h+ p0

Compressible fluid:

dpdz

= ! gpRT

and integrate w.r.t ( p, z).

Manometer rules: (! "ve)(# +ve); dp

dx= dp

dy= 0; pv if evacuated; $ gas % 0.