What
is Hydrostatic Pressure Fluid Pressure and Depth
The air
around us at sea level presses down on us at 14.5 pounds per
square inch (1 bar). We do not feel this pressure since the
fluids in our body are pushing outward with the same force.
But if you swim down into the ocean just a few feet and you
will start to notice a change. You will start to feel an increase
of pressure on your eardrums.
This is because of an increase in hydrostatic pressure which
is the force per unit area exerted by a liquid on an object.
The deeper you go under the sea, the greater the pressure
pushing on you will be. For every 33 feet (10.06 meters) you
go down, the pressure increases by 14.5 psi (1 bar).
Hydrostatic
pressure is the pressure that is exerted by a fluid at equilibrium
at a given point within the fluid, due to the force of gravity.
Hydrostatic pressure increases in proportion to depth measured
from the surface because of the increasing weight of fluid
exerting downward force
from above.
If a
fluid is within a container then the depth of an object placed
in that fluid can be measured. The deeper the object is placed
in the fluid, the more pressure it experiences. This is because
the weight of the fluid is above it. The more dense the fluid
above it, the more pressure is exerted on the object that
is submerged, due to the weight of the fluid.
Let
us derive the formula for Pressure on a object submerged in
a fluid:
From, what
is pressure: Pressure = Force/Area
From, what
is Force: Force = mass x
acceleration = m x g (acceleration in gravity)
So: Pressure
= F/A = mg/A
From What
is Density: Density = Mass/Volume ; Mass= Density x Volume
We now
have Pressure = (density x volume x acceleration)/area.
The
formula that gives the P pressure on an object submerged
in a fluid is therefore:
P
= r * g * h
r
(rho) is the density of the fluid,
g is the acceleration of gravity
h is the height of the fluid above the object

The pressure
due to the liquid alone (i.e. the gauge pressure) at a given
depth depends only upon the density of the liquid, the acceleration
of gravity and the distance below the surface of the liquid.

The
static fluid fluid pressure at a given depth does not
depend upon the total mass, surface area, or the geometry
of the container.
P
= r * g * h
Pressure
= (density of liquid) x (acceleration gravity) x (height)
See more advanced readings about Static
Fluid Pressure from Georgia
State University Physics Dept. 
If the
container is open to the atmosphere above, the added atmospheric
pressure must be added if one is to find the total pressure
on an object. The pressure at a given depth in a static liquid
is a result the weight of the liquid acting on a unit area
at that depth plus any pressure acting on the surface
of the liquid.
Ptotal
= Patmosphere + Pfluid
Ptotal
= Patmosphere + ( r * g * h )
Example:
Find the pressure on a scuba diver who is 10 meters below
the surface of the ocean. Assume standard atmospheric conditions.
Use the density of sea water = 1.03 X 10^{3} kg/m^{3}
and the atmospheric pressure of 1.01 x 10^{5} N/m
^{2}.
Solution:
Pfluid
= r g h = (1.03 x10 3 kg/m3) (9.8 m/s^{2}) (10 m)
= 1.09 x 10^{5} N/m ^{2}.
Ptotal = Patmosphere + Pfluid = (1.01 x 10^{5}) +
(1.09 x 10^{5}) Pa = 2.10 x 10^{5} Pa ( Pascals)
Readings
and References
Hydrostatic
Pressure in a Liquid
Static
Fluid Pressure
Fluid
Pressure and Depth K12 Lesson from NASA
