FUNDAMENTALS
Static fluid is a fluid at rest or a fluid that moves as a rigid body meaning there
are no relative motion between adjacent fluid parcels
There are two types of forces that act upon the fluid: pressure force(short distance)
and gravitational force(long distance).
When a fluids velocity is zero, denoted as hydrostatic condition, the pressure variation
is due only to the weight of the fluid
Pressure
Pressure: is the normal force per unit area, pressure has no direction like temperature
and density therefore its not a vector, it is a scalar
÷
Pascals law
The pressure value in a point within a fluid at rest is independent of the orientation of
the plane containing the point
Pressure in a fluid at rest is an isotropic quantity, meaning its equal in all directions
or more accurately in the present case, independent of direction
Fluid at rest
JP
ay
=
=
Volume does not move
Sum of forces on the volume=0
Sum of force components=0
Forces are vectors meaning their direction matters in this case
Pressure distributions
Along the y axis and x axis the pressure gradient=0
Pressure remains constant when moving a point along the y or x direction
Pressure only varies along the direction of gravity
There is no pressure change in the horizontal directions and there is a vertical change
in pressure proportional to density, gravity and depth change
a=
y
y
:
-
y
=
-
pg
Specific weight
Fundamental equations
Pressure distribution is only dependent on density(distribution) and relative elevation
>
>
=
do
(z
d
=
-
:
pg
dp
.
=
-
pgd
Hydrostatic pressure distribution
Pressure increases with depth and density can be treated as a constant in this case
The pressure distribution in an incompressible fluid depends linearly only on the depth
The shape of the container does not play any role in calculation
Density will be the density of the fluid therefore it is constant everywhere within that
fluid and doesn't depend on the size
>
=
7
constant
?
32-31
was
=
pglzz -2
-
Moz
,
3- P1
=
-
pgh
-3
p ,=pz
+
pgh
Dz
-
=
pg
h is the height of a column of fluid of density p that establishes a pressure difference
of p1-p2: also referred to as pressure head
Worked example
Determine the pressure at the petrol/water
interface and at the bottom of the tank
PI
Po
:
=
=
2
p
:
,
-
-
P petrol
=
g
✗
0+749×9.81
Pz :-p water
=
✗
16,172
( H h
-
✗
(3-0.8)
=
16,172Pa
xgxh
(1000×9.81×0.8)
+
20,023Pa
Ideal gas
Density isn't the same but it is dependent on the temperature and the gas itself
dp
d
in
=
-
and
pg
%
.
=
-
p=R?
%-)?
Kamo
dz
Ten
d¥= 9k¥
-
Isothermal
Temperature is constant
R¥o(22-21
-
Pz =p
✗
,
e
=/ top
(2)
-
Bz
:
Linear variation of temperature with altitude
Manometers
Classified into Piezometer tubes, Utubes, and inclined tube manometers
Piezometer tubes are closed tank with a hole drilled perpendicularly to the surface,
the liquid will fill the L shaped tube until a certain elevation, h is measured and
P(A) is calculated which is the absolute/gauge pressure
liquid
PA
at
Patm
=
rest
+
g. =p ,g
p1gh
U-tubes have the capability to measure pressure in containers
with gas
Pressure on the left branch=pressure on the right branch
>
A +
Yih
if
,
=
the
Patm
+
fluid
Yzhz
in
the
Kno
Pa= Patm
container
+
is
Yzhz
gas
-
Yih
,
y
,
Yz
loaaaaaaa
PAE
patmtfzhz
Inclined-tube manometers are used for small pressure
differences
PA
-
PB I Yz lzsino
Small inclination amplify the reading l(2) for the
same pressure difference therefore more
accurate measurement for small pressure
differences
Summary
Pressure in a continuously distributed uniform static fluid varies only with vertical distance
and is independent of the shape of the container. The pressure is the same at all points on
a given horizontal plane in the fluid. The pressure increases with depth in the fluid.