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Hydrostatic Pressure
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 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)
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.
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 103 kg/m3and the atmospheric pressure of 1.01
x 105 N/m 2.
Solution:
Pfluid = r g h = (1.03 x10 3 kg/m3)
(9.8 m/s2) (10 m) = 1.09 x 105 N/m 2.
Ptotal = Patmosphere + Pfluid = (1.01 x 105) + (1.09 x 105) Pa = 2.10 x 105 Pa ( Pascals)
Ptotal = Patmosphere + Pfluid = (1.01 x 105) + (1.09 x 105) Pa = 2.10 x 105 Pa ( Pascals)
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