Fluid Mechanism - UPSC PDF Download

 Page 1


 
FLUID MECHANISM 
 
Hydrostatics: 
1. In a fluid that's not moving/ static fluid, the force per unit area at any spot stays 
the same no matter how you turn the surface. 
2. This force always acts ? er to the chosen surface. 
 
 Pressure =
?? ?
?? 
3. The value of force acting on a unit area at any point is called pressure at that 
point. 
4. Ideal fluids offer negligible resistance to tangential force. They cannot withstand 
tangential force. 
5. Since ideal fluid cannot sustain shear stress therefore in a steady state liquid 
remains ? to the " g
eff 
 ". VARIATION OF PRESSURE WITH DEPTH 
(i) Let pressure at L is P
1
 and pressure at M is P
2
 
Then, ?? 2
?? =?? 1
?? +?????? (?? 2
-?? 1
)??? 2
=?? 1
+???? (?? 2
-?? 1
) 
Here pressure gradient 
????
????
=???? 
(ii) Pressure is the same at two points in the same horizontal level. 
Page 2


 
FLUID MECHANISM 
 
Hydrostatics: 
1. In a fluid that's not moving/ static fluid, the force per unit area at any spot stays 
the same no matter how you turn the surface. 
2. This force always acts ? er to the chosen surface. 
 
 Pressure =
?? ?
?? 
3. The value of force acting on a unit area at any point is called pressure at that 
point. 
4. Ideal fluids offer negligible resistance to tangential force. They cannot withstand 
tangential force. 
5. Since ideal fluid cannot sustain shear stress therefore in a steady state liquid 
remains ? to the " g
eff 
 ". VARIATION OF PRESSURE WITH DEPTH 
(i) Let pressure at L is P
1
 and pressure at M is P
2
 
Then, ?? 2
?? =?? 1
?? +?????? (?? 2
-?? 1
)??? 2
=?? 1
+???? (?? 2
-?? 1
) 
Here pressure gradient 
????
????
=???? 
(ii) Pressure is the same at two points in the same horizontal level. 
 
As body is in equilibrium, P
1
 A=P
2
 A?P
1
=P
2
 
{Note : Pressure ?? is independent of shape of container} 
 
P
 absolute 
 Pressure 
=P
0
+ ???? gh
?  
yauge pressure 
 
 
i.e. diff. from atmospheric pressure 
? In terms of water coloumn 
=1 atm pressure 
 
 
Page 3


 
FLUID MECHANISM 
 
Hydrostatics: 
1. In a fluid that's not moving/ static fluid, the force per unit area at any spot stays 
the same no matter how you turn the surface. 
2. This force always acts ? er to the chosen surface. 
 
 Pressure =
?? ?
?? 
3. The value of force acting on a unit area at any point is called pressure at that 
point. 
4. Ideal fluids offer negligible resistance to tangential force. They cannot withstand 
tangential force. 
5. Since ideal fluid cannot sustain shear stress therefore in a steady state liquid 
remains ? to the " g
eff 
 ". VARIATION OF PRESSURE WITH DEPTH 
(i) Let pressure at L is P
1
 and pressure at M is P
2
 
Then, ?? 2
?? =?? 1
?? +?????? (?? 2
-?? 1
)??? 2
=?? 1
+???? (?? 2
-?? 1
) 
Here pressure gradient 
????
????
=???? 
(ii) Pressure is the same at two points in the same horizontal level. 
 
As body is in equilibrium, P
1
 A=P
2
 A?P
1
=P
2
 
{Note : Pressure ?? is independent of shape of container} 
 
P
 absolute 
 Pressure 
=P
0
+ ???? gh
?  
yauge pressure 
 
 
i.e. diff. from atmospheric pressure 
? In terms of water coloumn 
=1 atm pressure 
 
 
(iii) 
 
M-1:   In ground frame 
 
(?? 2
-?? 1
)?? =???????? ?? 2
=?? 1
+?????? 
M-2: ( g
eff 
 component) distance 
 
tan ?? =
a
g
=
h
t
 
P
0
+???? h=P
1
 
?? 0
+?????? =?? 
 
Example. 
 
Page 4


 
FLUID MECHANISM 
 
Hydrostatics: 
1. In a fluid that's not moving/ static fluid, the force per unit area at any spot stays 
the same no matter how you turn the surface. 
2. This force always acts ? er to the chosen surface. 
 
 Pressure =
?? ?
?? 
3. The value of force acting on a unit area at any point is called pressure at that 
point. 
4. Ideal fluids offer negligible resistance to tangential force. They cannot withstand 
tangential force. 
5. Since ideal fluid cannot sustain shear stress therefore in a steady state liquid 
remains ? to the " g
eff 
 ". VARIATION OF PRESSURE WITH DEPTH 
(i) Let pressure at L is P
1
 and pressure at M is P
2
 
Then, ?? 2
?? =?? 1
?? +?????? (?? 2
-?? 1
)??? 2
=?? 1
+???? (?? 2
-?? 1
) 
Here pressure gradient 
????
????
=???? 
(ii) Pressure is the same at two points in the same horizontal level. 
 
As body is in equilibrium, P
1
 A=P
2
 A?P
1
=P
2
 
{Note : Pressure ?? is independent of shape of container} 
 
P
 absolute 
 Pressure 
=P
0
+ ???? gh
?  
yauge pressure 
 
 
i.e. diff. from atmospheric pressure 
? In terms of water coloumn 
=1 atm pressure 
 
 
(iii) 
 
M-1:   In ground frame 
 
(?? 2
-?? 1
)?? =???????? ?? 2
=?? 1
+?????? 
M-2: ( g
eff 
 component) distance 
 
tan ?? =
a
g
=
h
t
 
P
0
+???? h=P
1
 
?? 0
+?????? =?? 
 
Example. 
 
 
?
 In terms of ?? 1
,?? ,?? ,?? ,h
?? 1
+???? h=?? 2
?? 1
+?????? cos ?? +?????? sin ?? =?? 5
??? 1
+?????? =?? 4
 ??? 1
+???? h+?????? =?? 3
 
 
 
 
Solution: ? ?? 1
+?? (
2?? 3
)h=?? 2
 
?? 2
-?? 1
=
2
3
???? h 
Example. Find tan ?? 
 
Solution: ?
g:????
] ]
?? ?tan ?? =
a
g
 ?? =tan
-1
 (
a
g
) 
Page 5


 
FLUID MECHANISM 
 
Hydrostatics: 
1. In a fluid that's not moving/ static fluid, the force per unit area at any spot stays 
the same no matter how you turn the surface. 
2. This force always acts ? er to the chosen surface. 
 
 Pressure =
?? ?
?? 
3. The value of force acting on a unit area at any point is called pressure at that 
point. 
4. Ideal fluids offer negligible resistance to tangential force. They cannot withstand 
tangential force. 
5. Since ideal fluid cannot sustain shear stress therefore in a steady state liquid 
remains ? to the " g
eff 
 ". VARIATION OF PRESSURE WITH DEPTH 
(i) Let pressure at L is P
1
 and pressure at M is P
2
 
Then, ?? 2
?? =?? 1
?? +?????? (?? 2
-?? 1
)??? 2
=?? 1
+???? (?? 2
-?? 1
) 
Here pressure gradient 
????
????
=???? 
(ii) Pressure is the same at two points in the same horizontal level. 
 
As body is in equilibrium, P
1
 A=P
2
 A?P
1
=P
2
 
{Note : Pressure ?? is independent of shape of container} 
 
P
 absolute 
 Pressure 
=P
0
+ ???? gh
?  
yauge pressure 
 
 
i.e. diff. from atmospheric pressure 
? In terms of water coloumn 
=1 atm pressure 
 
 
(iii) 
 
M-1:   In ground frame 
 
(?? 2
-?? 1
)?? =???????? ?? 2
=?? 1
+?????? 
M-2: ( g
eff 
 component) distance 
 
tan ?? =
a
g
=
h
t
 
P
0
+???? h=P
1
 
?? 0
+?????? =?? 
 
Example. 
 
 
?
 In terms of ?? 1
,?? ,?? ,?? ,h
?? 1
+???? h=?? 2
?? 1
+?????? cos ?? +?????? sin ?? =?? 5
??? 1
+?????? =?? 4
 ??? 1
+???? h+?????? =?? 3
 
 
 
 
Solution: ? ?? 1
+?? (
2?? 3
)h=?? 2
 
?? 2
-?? 1
=
2
3
???? h 
Example. Find tan ?? 
 
Solution: ?
g:????
] ]
?? ?tan ?? =
a
g
 ?? =tan
-1
 (
a
g
) 
 
a is slowly ? from 0 to 
?? 3
 
mi volume of liquid remaining inside beaker? 
Solution: 
 
tan ?? =
a
g
=
1
3
 ?  volume out =( Area )×t=(
1
2
×
t
3
×t)×t?
t
3
6
 
?  Volume remaining =t
3
-
t
3
6
=
5t
3
6
 
from 0 to 
3 g
2
 ? 
when acc. is 'g' 
But when acc. is 
3?? 2