MMVF01 Termodynamik och strömningslära FORMELSAMLING till

Institutionen f¨
or Energivetenskaper
MMVF01
Termodynamik och stro
ara
¨mningsl¨
FORMELSAMLING
till
D. F. Young, B. R. Munson, T. H. Okiishi & W. W. Huebsch,
A Brief Introduction to Fluid Mechanics,
John Wiley & Sons, Inc.
Sammanst¨alld av
Christoffer Norberg
juni 2011
Kapitel 3 — Bernoullis ekvation
Betrakta, enligt figuren nedan, en fluidpartikel som f¨oljer en str¨omlinje i tv˚
adimensionell, station¨ar, och friktionsfri str¨omning (endast tryck- och gravitationskrafter).
Hastighetsvektor: Vs = V =
ds
, Vn = 0
dt
∂V
V2
Accelerationsvektor: as = V
, an =
∂s
R
dp + ρ d (V 2 /2) + ρ g dz = 0 (l¨angs str¨omlinjen)
Inkompressibel stro¨mning ⇒
p + ρ V 2/2 + ρ g z = konst. (l¨angs str¨omlinjen)
p = statiskt tryck (faktiskt tryck); ρ V 2 /2 = dynamiskt tryck;
ρ g z = γ z = h¨ojdtryck.
dz
dp ρ V 2
+
+ ρg
= 0 (tv¨ars str¨omlinjen)
dn
R
dn
Inkompressibel str¨omning ⇒
p+ρ
R V2
R
dn + ρ g z = konst. (tv¨ars str¨omlinjen)
1
• Ekvivalent ytr˚
ahet ǫ (nya ro¨r, typiska va¨rden):
Material (Sv.)
Glas
Plast (PVC), draget
M¨
assing, draget
Rostfritt st˚
al
Gummi
Kommersiellt st˚
al
Smidesj¨
arn
Bleckpl˚
at, sl¨
at
Galvaniserat j¨
arn
Tr¨
a, hyvlat
Gjutj¨
arn
Betong, glatt
Betong, skrovlig
Nitat st˚
al
Material (Eng.)
Glass
Drawn tubing
Brass, drawn
Stainless steel
Rubber
Commercial steel
Wrought iron
Tinplate, smooth
Galvanized iron
Wood, planed
Cast iron
Concrete, smooth
Concrete, rough
Riveted steel
ǫ [mm]
0.0 (sl¨att)
0.0015
0.002
0.002
0.010
0.046
0.046
0.07
0.15
0.18–0.9
0.26
0.3–0.8
1.2–3.0
0.9–9.0
• Eng˚
angsfo
¨rluster (eng. minor losses)
∆pf ,minor = KL
ρV 2
V2
= ρghL,minor ⇒ hL,minor = KL
2
2g

ℓ
ρ X
f
R¨
orsystem: ∆pf = ∆pf ,major +∆pf ,minor = 
2 i
D
2
!
i
Vi2 +
(8.20)
X
j

(KL)j Vj2
ORDLISTA
English
absolute pressure
adverse pressure gradient
average velocity
basic dimension
boundary layer
bulk modulus
buoyant force, buoyancy
continuity equation
control volume
Couette flow
crude oil
density
discharge coefficient
displacement thickness
drag
drag coefficient
dynamic (absolute) viscosity
dynamic pressure
elbow
entrance region
friction factor
frontal area
gage pressure
head loss
heat transfer rate
hydraulic diameter
irrotational flow
kinematic viscosity
laminar flow
linear momentum equation
loss coefficient
Mach number
mass flowrate
material (substantial) derivative
major loss
minor loss
moment-of-momentum equation
momentum thickness
nozzle meter
orifice meter
pathline
pipe flow
Pitot-static tube
planform area
Poiseuille flow
svenska
absoluttryck (relativt vakuum)
ogynnsam tryckgradient
medelhastighet
prim¨ar dimension
gr¨ansskikt
bulkmodul (tryckmodul)
flytkraft
kontinuitetsekvationen
kontrollvolym, o¨ppet system
Couettestr¨omning
r˚
aolja
densitet
genomstr¨omningskoefficient
f¨ortr¨angningstjocklek
str¨omningsmotst˚
and
motst˚
andskoefficient
dynamisk viskositet
dynamiskt tryck
r¨orb¨oj, r¨orkr¨ok
inloppsstr¨acka
friktionsfaktor
frontarea
¨overtryck (relativt omgivande tryck)
h¨ojdf¨orlust
v¨armefl¨ode
hydraulisk diameter
rotationsfri str¨omning
kinematisk viskositet
lamin¨ar str¨omning
impulssatsen
eng˚
angsf¨orlustkoefficient
machtal (Machs tal)
massfl¨ode
materiell derivata
h¨ojd- eller tryckf¨orlust p.g.a. v¨aggfriktion
eng˚
angsf¨orlust
impulsmomentsatsen
impulsf¨orlusttjocklek
strypfl¨ans
strypbricka
partikelbana
r¨orstr¨omning
Prandtlr¨or
planarea
Poiseuillestr¨omning
3
avsnitt
1.5, 2.5
9.2.6
5.1.1, 8.2
7.1
9.2
1.7.1
2.11.1
3.6.2, 5.1, 6.2.1
4.3
6.9.2
1.6, 8.5
1.4.1
8.6
9.2.1
9.1.1
7.9.2, 9.1.1
1.6
3.5
8.4.2
8.1.2
8.4.1
9.1.1
1.5, 2.5
5.3.3
5.3.1
8.4.3
6.1.3, 6.4.3
1.6
4.1.3, 8.1.1
5.2.1/2
8.4.2
3.8, 7.6
5.1.1
4.2.1, 6.1.1
8.4.1
8.4
5.2.3/4
9.2.1
3.6.3, 8.6
3.6.3, 8.6
4.1.4
8.1
3.5
9.1.1
6.9.3
pressure coefficient
pressure drag, form drag
pump head
rate of shearing strain
repeating variables
Reynolds number
separation
shaft power
shaft torque
siphon
specific gravity
specific volume
specific weight
speed of sound
sluice gate
steady flow
streakline
streamline
surface tension
system
turbulent flow
vacuum pressure
valve
vapor pressure
velocity head
Venturi meter
volume flow rate
volumetric dilatation rate
vorticity
wall shear stress
tryckkoefficient
formmotst˚
and
pumph¨ojd
skjuvt¨ojningshastighet
repeterande variabler
Reynolds tal
avl¨osning
axeleffekt
vridmoment
sugh¨avert (h¨avert)
relativ densitet
volymitet
tyngd per volymsenhet
ljudhastighet
slussport
station¨ar str¨omning
str˚
aklinje
str¨omlinje
ytsp¨anning
slutet system
turbulent str¨omning
undertryck (relativt omgivande tryck)
ventil
˚
angtryck
hastighetsh¨ojd
venturimeter
volymfl¨ode
volymsdilatation
vorticitet
v¨aggskjuvsp¨anning
4
9.3.2
9.3.2
5.3.3
6.1.3
7.3
7.6
9.1.2/6
5.2.4
5.2.4
3.6.2
1.4.3
1.4.1
1.4.2
1.7.3
3.6.3, 10.6.4
4.1.3
4.1.4
4.1.4
1.9
4.3
4.1.3, 8.1.1
2.5
8.4.2
1.8
3.4
3.6.3, 8.6
5.1.1
6.1.2
6.1.3
8.2.1