Hydrostatic
pressure
Everything in the universe exerts some pressure on each
other which could be large or negligible it depends on the force, acceleration,
and gravity.
Such Atmospheric pressure
decreases as the altitude increases because the air particles or mess ( that
exerts force and pressure increase) decreases as we go upward. So, that is the
reason atmosphere pressure decreases as we go up.
Air surrounds us exerts pressure on but we don’t feel it because the fluids inside us are also exerted equal pressure toward that to keep the balance.
Before understanding hydrostatics, we must need to know
about basic terms which may help out to better understanding hydrostatics.
What is hydrostatic?
Hydrostatic: hydrostatic is the branch of fluid
statics that deal with all fluid, both compressible and incompressible fluid at
rest.
Pressure: when
the body is immersed in a fluid, the pressure is exerted by a fluid or in a
fluid on the body.
Hydrostatics has vast application in almost every field such
as geophysics ( for measuring atmospheric pressure) in biology ( for measuring
blood pressure) in engineering ( for equipment to store and transport the
fluids) in many other fields.
Pressure in fluids at rest:
The pressure on a fluid at rest is called isotropic. If the
fluid is at rest then,
·
The pressure on each side of fluid must be equal
·
The pressure is normal to any contacting
surface.
A fluid cannot remain at rest under the presence of shear
stress due to the fundamental nature of the fluid.
Pressure in fluid not at rest:
if the fluid is not at rest then
·
The fluid will move in the direction of the
resulting force
·
Fluid transfer force from one to another.
How the hydrostatic pressure is produced?
If you immerse a body into fluid, the body experiences pressure.
The depth of a body's place in that fluid can be measured. When the body goes
down, the more pressure it experiences due to the weight of the fluid above it.
Due to the weight of the fluid the more the fluid above the body the more it
experiences pressure on the submerged body. Due to the force of gravity, the
hydrostatic pressure is exerted by the fluid which is at equilibrium within the
fluid. Hydrostatic pressure is increased as the depth measured from the surface
increases due to the increasing weight of the fluid above the body.
What is hydrostatic pressure?
If a fluid is at rest, all inertial and frictional stresses
vanish, that state of the system is called hydrostatic. When this condition is
satisfied the gradient of pressure becomes a function of force only
In a conservation
force field a gravitational force field, the pressure exerted by a fluid at
equilibrium becomes a function of force exerted by gravity.
Hydrostatic Pressure definition:
“Hydrostatic pressure is the pressure that is exerted by
the fluid at equilibrium at a given point within the fluid due to force of
gravity.”
Hydrostatic pressure increases in proportion to the depth measured from the surface because of the weight of fluid which is increasing downward.
Give examples of hydrostatic pressure?
A few examples of hydrostatic pressure are
·
If you swim down into the ocean, you will feel an
increase in pressure due to an increase in hydrostatic pressure which is the
force per unit exerted by a liquid on an object. Every 33 feet (10.06) you go
down the pressure increase by 14.5 psi. The deeper you go underwater, the
increase in hydrostatic pressure you will feel.
·
Consider a layer of water in any container. The
sides of the container exerted pressure on the layers of water. There is more
pressure on the lower layer of water because the pressure exerted by the top
layer on the lower adds up.
What is the mathematical equation of hydrostatic
pressure?
Consider a control volume of an infinitesimally small cube
of fluid. The only force acting on a cube of fluid is the weight of the fluid
above it. The hydrostatic pressure can be calculated as
P(z) -P(z0)= 1/A
Where:
·
P= is the hydrostatic pressure (pa)
·
A=is the test area (m^2)
·
Z=is the height ( parallel to the direction of
gravity) of the test area (m)
·
Z0=is the height of the zero reference point of
the pressure
·
g= is the gravitational accerlation( m/s^2)
·
P=is the fluid density (kg/m^3)
For incompressible fluids (water and other liquids):
Assuming a constant density of liquids throughout the liquid and the incompressible nature of the liquid, the integral can be simplified significantly for many applications.
Since the height h of the fluid between z and z0 is
reasonably small as compared to the radius of the earth, one can neglect the
variation of g. In this way, the integral is simplified into the formula
P -p0 = pgh
Where:
h = is
the height z-z0 between the test volume
and zero reference point of the pressure.
This reference point should lie at or below the surface of
the liquid, otherwise one has to spill the integral into two terms with the
constant P liquid and p (z’) above. The absolute pressure compared to vacuum is
P = Pgh + p atm
P atm = is the atmospheric pressure
H = is the total height of the liquid above the test area to
the surface
Application of hydrostatic pressure:
There are many applications of hydrostatic pressure and all
of them have separate equations
Hydrostatic force on submerged surfaces :
The hydrostatic force acting on a submerged surface has a vertical
and horizontal component
Fh = pc A
Fv = pgv
Where:
Pc = is the pressure at the centroid of the vertical
projection of the submerged surface
A = is the area of the same vertical projection of the
surface
P = is the density of the fluid
G = is the acceleration due to gravity
V = is the volume of
fluid directly above the curved surface
Atmospheric pressure:
For a pure ideal gas of constant temperature in a
gravitational field is T, its pressure P, will vary with height, h, as;
P (h) = P (0) e -Mgh/kT
This is known as the barometric formula, assuming the
pressure is hydrostatic.
g = is the acceleration due to gravity
T = is the absolute temperature
M = is the mass of a single molecule of gas
K = is the Boltzmann constant
h = is the height
p = is the pressure
For multiple gases:
If there are multiple types of gases, then the partial
pressure of each gas will be given by the equation. The distribution of each
species of gas is independent of the other species.
Buoyancy :
If a body of arbitrary shape is immersed, partly or fully in
a fluid it will experience the action of a net force in the opposite direction
of the pressure gradient. If this pressure gradient arises from gravity, the
net force is in the vertical direction that of the gravitational force.
This vertical force is termed buoyancy force or is equal in
magnitude, but opposite in direction to the weight of the displaced fluid.
Mathematically,
F =pgv
Where;
P = is the density of
the fluid
G = is the acceleration due to gravity
V= is the volume of fluid directly above the curved surface
For example:
For a ship, its weight is balanced by pressure forces from
the surrounding water which allows it to float. If more cargo is loaded onto a ship,
it would sink more into the water for displacing more water and receive a
higher buoyant force to balance the increased weight.
Medicine:
In medicine, hydrostatic pressure is used to measure blood
pressure. The pressure in blood vessels is due to the pressure of the fluid
against the wall.
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