Formula Sheet: Fluid Properties | Fluid Mechanics for Mechanical Engineering PDF Download

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Fluid Prop erties F orm ula Sheet
Basic Fluid Prop erties
• Densit y (? ) : Mass p er unit v olume.
?=
m
V
(Units: kgm
-3
)
where m is mass, V is v olume.
• Sp ecific W eigh t ( ? ) : W eigh t p er unit v olume.
? =?g (Units: Nm
-3
)
where g is gra vitational acceleration (981m/s
2
).
• Sp ecific Gra vit y ( SG ) : Ratio of fluid densit y to w ater densit y .
SG=
?
fluid
?
w ater
(Dimensionless)
where ?
w ater
=1000kgm
-3
.
• Relativ e Densit y : Same as sp ecific gra vit y .
Viscosit y
• Dynamic Viscosit y (µ ) : Measure of a fluid’s resistance to shear flo w.
t =µ
du
dy
(Newton’s La w of Viscosit y)
where t is she ar stress (Pa ),
du
dy
is the v elo cit y g radien t (s
-1
), µ is in Pas .
• Kinematic Viscosit y (? ) : Ratio of dynamic viscosit y to densit y .
? =
µ
?
(Units: m
2
s
-1
)
• Viscosit y V ariation : F or liquids,µ decreases with temp erature; for gases,µ increases
with temp erature.
Surface T ension
• Surface T ension (s ) : F orce p er unit length due to molecular cohesion.
s =
F
L
(Units: Nm
-1
)
where F is the force, L is the length of the in terface.
• Pressure Difference A cross Curv ed Surface : Due to surface tension.
?P =
2s
R
(for a spherical droplet)
?P =
s
R
(for a soap bubble, t w o s urfaces)
where R is the radius of curv ature (m ).
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Fluid Prop erties F orm ula Sheet
Basic Fluid Prop erties
• Densit y (? ) : Mass p er unit v olume.
?=
m
V
(Units: kgm
-3
)
where m is mass, V is v olume.
• Sp ecific W eigh t ( ? ) : W eigh t p er unit v olume.
? =?g (Units: Nm
-3
)
where g is gra vitational acceleration (981m/s
2
).
• Sp ecific Gra vit y ( SG ) : Ratio of fluid densit y to w ater densit y .
SG=
?
fluid
?
w ater
(Dimensionless)
where ?
w ater
=1000kgm
-3
.
• Relativ e Densit y : Same as sp ecific gra vit y .
Viscosit y
• Dynamic Viscosit y (µ ) : Measure of a fluid’s resistance to shear flo w.
t =µ
du
dy
(Newton’s La w of Viscosit y)
where t is she ar stress (Pa ),
du
dy
is the v elo cit y g radien t (s
-1
), µ is in Pas .
• Kinematic Viscosit y (? ) : Ratio of dynamic viscosit y to densit y .
? =
µ
?
(Units: m
2
s
-1
)
• Viscosit y V ariation : F or liquids,µ decreases with temp erature; for gases,µ increases
with temp erature.
Surface T ension
• Surface T ension (s ) : F orce p er unit length due to molecular cohesion.
s =
F
L
(Units: Nm
-1
)
where F is the force, L is the length of the in terface.
• Pressure Difference A cross Curv ed Surface : Due to surface tension.
?P =
2s
R
(for a spherical droplet)
?P =
s
R
(for a soap bubble, t w o s urfaces)
where R is the radius of curv ature (m ).
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Capillarit y
• Capillary Rise/F all : Heigh t of liquid in a capillary tub e.
h=
2scos?
?gr
where h is the heigh t of rise/fall (m ), ? is the con tact angle, r is the tub e radius (m ).
• Notes :
– ? <90
?
: Capillary rise (e.g., w ater in glass).
– ? >90
?
: Capillary fall (e.g., mercury in glass).
Compressibilit y and Bulk Mo dulus
• Bulk Mo dulus (K ) : Measure of a fluid’s resistance to compression.
K =-
?P
?V/V
(Units: Pa )
where ?P is the c hange in pressure, ?V/V is the v olumetric s train.
• Compressibilit y : In v erse of bulk mo dulus.
ß =
1
K
(Units: Pa
-1
)
• Sp eed of Sound in Fluid : Related to compressibilit y .
c=
v
K
?
(Units: ms
-1
)
V ap or Pressure and Ca vitation
• V ap or Pressure : Pressure at whic h a liquid v ap orizes.
P
v
(V aries with temp erature, Pa )
• Ca vitation : Occurs when fluid pressure drops b elo w v ap or pressure, causing bubble
formation.
Key Notes
• Standard v alues: ?
w ater
=1000kgm
-3
, ?
w ater
=9810Nm
-3
, g =9.81ms
-2
.
• T ypical v alues: µ
w ater
˜0.001Pas , ?
w ater
˜1×10
-6
m
2
s
-1
at 20
?
C .
• Surface tension: s
w ater
˜0.073Nm
-1
at 20
?
C .
• Use SI units for calculations.
• F or capillarit y , ensure ? is consisten t wi th the fluid-tub e com bination.
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