Page 1
Fluid Statics
2
Fluid Statics: It is the branch of fluid mechanics that deals
with the behavior/response of fluid when they are at rest.
Pressure, (average pressure intensity): It is the normal force
exerted per unit area. It is denoted by P and is given by;
Units
SI: N/m
2
(called Pascal)
BG: lb/ft
2
or lb/in
2
(called psi)
CGS: dyne/cm
2
1 bar=10
5
N/m
2
=10
5
Pascal
A
F
area
force
P = =
Page 2
Fluid Statics
2
Fluid Statics: It is the branch of fluid mechanics that deals
with the behavior/response of fluid when they are at rest.
Pressure, (average pressure intensity): It is the normal force
exerted per unit area. It is denoted by P and is given by;
Units
SI: N/m
2
(called Pascal)
BG: lb/ft
2
or lb/in
2
(called psi)
CGS: dyne/cm
2
1 bar=10
5
N/m
2
=10
5
Pascal
A
F
area
force
P = =
Pressure vs Water depth/height
3
Consider a strip or column of a cylindrical fluid,
h= height or depth of strip of fluid
?= specific weight of fluid
dA=cross-sectional area of strip
dV=volume of strip
dW=weight of strip
Pressure at base of strip=dF/dA=dW/dA
P= ?dV/dA
P= ?dA.h/dA
P=?h
h
Page 3
Fluid Statics
2
Fluid Statics: It is the branch of fluid mechanics that deals
with the behavior/response of fluid when they are at rest.
Pressure, (average pressure intensity): It is the normal force
exerted per unit area. It is denoted by P and is given by;
Units
SI: N/m
2
(called Pascal)
BG: lb/ft
2
or lb/in
2
(called psi)
CGS: dyne/cm
2
1 bar=10
5
N/m
2
=10
5
Pascal
A
F
area
force
P = =
Pressure vs Water depth/height
3
Consider a strip or column of a cylindrical fluid,
h= height or depth of strip of fluid
?= specific weight of fluid
dA=cross-sectional area of strip
dV=volume of strip
dW=weight of strip
Pressure at base of strip=dF/dA=dW/dA
P= ?dV/dA
P= ?dA.h/dA
P=?h
h
Pressure vs Water depth/height
4
P=?h
P a h
For h=0, P=0
For h=h, P=?h
h
Pressure distribution
diagram/pressure profile
As you know atmospheric pressure reduces, as we move to
higher elevations. Is it because of h, as h reduces, P also reduces.
Page 4
Fluid Statics
2
Fluid Statics: It is the branch of fluid mechanics that deals
with the behavior/response of fluid when they are at rest.
Pressure, (average pressure intensity): It is the normal force
exerted per unit area. It is denoted by P and is given by;
Units
SI: N/m
2
(called Pascal)
BG: lb/ft
2
or lb/in
2
(called psi)
CGS: dyne/cm
2
1 bar=10
5
N/m
2
=10
5
Pascal
A
F
area
force
P = =
Pressure vs Water depth/height
3
Consider a strip or column of a cylindrical fluid,
h= height or depth of strip of fluid
?= specific weight of fluid
dA=cross-sectional area of strip
dV=volume of strip
dW=weight of strip
Pressure at base of strip=dF/dA=dW/dA
P= ?dV/dA
P= ?dA.h/dA
P=?h
h
Pressure vs Water depth/height
4
P=?h
P a h
For h=0, P=0
For h=h, P=?h
h
Pressure distribution
diagram/pressure profile
As you know atmospheric pressure reduces, as we move to
higher elevations. Is it because of h, as h reduces, P also reduces.
PASCAL’S LAW
5
“Pressure at any point in fluid is same in all directions when
the fluid is at rest”
Consider a wedge shape element of fluid
having dimension dx, dy and dz along x, y
and z axis.
dl= dimension of inclined plane making
an angle a with the vertical
Px, Py, Pz and P are pressure acting in x, y,
z and perpendicular to inclined surface
dW=weight of element
z
y
x
Py(dxdz)
Px(dydz)
P(dldz)
dx
dy
dz
a
a
a
P(dldz)
cosa
P(dldz)
sina
dW
z
y
x
Page 5
Fluid Statics
2
Fluid Statics: It is the branch of fluid mechanics that deals
with the behavior/response of fluid when they are at rest.
Pressure, (average pressure intensity): It is the normal force
exerted per unit area. It is denoted by P and is given by;
Units
SI: N/m
2
(called Pascal)
BG: lb/ft
2
or lb/in
2
(called psi)
CGS: dyne/cm
2
1 bar=10
5
N/m
2
=10
5
Pascal
A
F
area
force
P = =
Pressure vs Water depth/height
3
Consider a strip or column of a cylindrical fluid,
h= height or depth of strip of fluid
?= specific weight of fluid
dA=cross-sectional area of strip
dV=volume of strip
dW=weight of strip
Pressure at base of strip=dF/dA=dW/dA
P= ?dV/dA
P= ?dA.h/dA
P=?h
h
Pressure vs Water depth/height
4
P=?h
P a h
For h=0, P=0
For h=h, P=?h
h
Pressure distribution
diagram/pressure profile
As you know atmospheric pressure reduces, as we move to
higher elevations. Is it because of h, as h reduces, P also reduces.
PASCAL’S LAW
5
“Pressure at any point in fluid is same in all directions when
the fluid is at rest”
Consider a wedge shape element of fluid
having dimension dx, dy and dz along x, y
and z axis.
dl= dimension of inclined plane making
an angle a with the vertical
Px, Py, Pz and P are pressure acting in x, y,
z and perpendicular to inclined surface
dW=weight of element
z
y
x
Py(dxdz)
Px(dydz)
P(dldz)
dx
dy
dz
a
a
a
P(dldz)
cosa
P(dldz)
sina
dW
z
y
x
PASCAL’S LAW
6
Py(dxdz)
Px(dydz)
P(dldz)
a
a
P(dldz)
cosa
P(dldz)
sina
P P
o dy dz P dydz P
dl dy o dl dy dldz P dydz P
o dldz P dydz P
F
x
x
x
x
x
=
= -
= = -
= -
=
?
) (
/ cos / ) (
cos ) (
0
a
a
Q
dW
P P
o dx dz P dxdz P
dw dl dx o dl dx dldz P dxdz P
o dldz P dW dxdz P
F
y
y
y
y
y
=
= -
? = = -
= - -
=
?
) (
0 & / sin / ) (
sin ) (
0
a
a
Q
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