EME 303 F LUID MECHANICS SUMMARIZED …elsworth/courses/eme_303/exam...EME 303 Fluid Mechanics 33©...
Transcript of EME 303 F LUID MECHANICS SUMMARIZED …elsworth/courses/eme_303/exam...EME 303 Fluid Mechanics 33©...
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.