Hydrostatic Pressure Video Lecture | Fluid Mechanics for Civil Engineering - Civil Engineering (CE)

this is the third lecture in this course
on fluid mechanics today I'll be talking
about hydrostatic pressure the learning
objective is to understand how the
pressure in the fluid relates to its
depth before discussing pressure in the
context of fluids let me first start by
giving an example of it in the context
of classical mechanics for those of you
who have not yet studied classical
mechanics this example will hopefully
make the concept of pressure a little
easier to understand so what is pressure
pressure is a measure of how
concentrated of forces mathematically
it's represented as force divided by the
surface area through which the force is
acting let's look at two situations in
the first a 50 kilogram weight is
resting on a table in the second a 50
kilogram weight is resting on a small
wooden block of negligible mass which is
then resting on the table the force on
the table caused by the object's weight
is 50 kilograms times 9.8 meters per
second squared or 490 Newtons this will
be the same in both situations however
in the left side example that force is
distributed to the table over the
relatively large surface area of the
bottom surface of the weight itself and
thus the pressure on the table will be
relatively low well in the right hand
example the force is distributed through
the much smaller surface area of the
block and thus the pressure on the table
will be relatively high in fluent
mechanics instead of one solid object
imparting pressure against another solid
object we have a fluid imparting
pressure against a solid but the concept
of a force per unit area is the same
when talking about fluids there are a
number of different types of pressure
that one can discuss the most
fundamental and important of these is
something called the hydrostatic
pressure this is the pressure present
within the fluid when it's at rest it
acts equally in all directions and it
acts at a right angle to any surface
that is in contact with the fluid so if
we have a glass of water
at a given level within the water the
hydrostatic pressure which is a result
of the weight of fluid above it acts on
the side of the glass equally in all
directions since pressure is the force
divided by area if the pressure was
somehow unequal it would mean the forces
on the glass were unequal which would
consequently result in the glass of
water moving and of course we know that
a glass of water at rest does not start
to slide laterally on its own as another
example of this imagine taking a playing
card and submerging it vertically into
the water the hydrostatic pressure in
the water will act at a right angle to
any surface in contact with the fluid
that means that there is a right-sided
pressure pushing on the left side of the
card and a left side of pressure pushing
on the right side of the card as these
forces are equal the card will not
spontaneously move in either direction
keep in mind however that just because
there is no net lateral force in the
card caused by the hydrostatic pressure
does not mean there is no net force of
any kind on it from the last lesson we
know that there is still the card's
weight and the cards buoyancy so unless
the card is exactly the same density as
water it will still move either up or
down within the water once released is
there any way to quantify the
hydrostatic pressure common experience
might tell us that the pressure in fluid
increases at increasing depth for
example when you jump into a deep
swimming pool if you've ever dived deep
down underwater you've probably felt the
pressure increasing as you go down
deeper and deeper quantitatively this
pressure increase can be calculated with
this equation the difference in pressure
between two points is equal to the
density of the fluid times little G
times the difference in vertical height
between the two points in the case of
the glass of water here if we were
interested in the pressure at the bottom
the two points we would use would be its
bottom and top the pressure at the top
is equal to atmospheric pressure and the
difference in vertical height is just
the depth of the water to refer back to
the last lesson on Archimedes principle
and buoyancy some of you might realize
that the buoyant force on a submerged
object which we said was equal to
density of the fluid times volume of the
displaced fluid times G is simply a
manifestation of the difference in
hydrostatic pressure that's acting
upwards on the bottom side of the object
and the hydrostatic pressure that's
acting downwards on the top side of the
object an interesting consequence of
this hydrostatic pressure equation which
may or may not be immediately obvious is
that the pressure at any given depth is
independent of the shape of the
container or the path that the pressure
must be transmitted along for example I
could have a collection of rare and
exotic jellyfish that I want to display
in my home but to highlight their
uniqueness maybe I want to build an
equally unique aquarium system in which
to house them if I wanted to know what
the maximum water pressure was at the
bottom of the system of tanks the only
thing that would matter is the total
vertical distance between the top and
bottom the shape of the tanks the volume
of the tanks the width and length of the
connecting tubes are all irrelevant also
notice that the lower tank needs a
sealed lid if the lid was not there the
weight of the water in the upper tank
would cause the lower tank to overflow
this is an example of a principle
frequently paraphrased that fluids at
rest seek their own level this means the
surface of any fluid at rest will have
the same height above the surface of the
earth at all points let's look at a
quantitative real world example of
hydrostatic pressure we have a house at
the bottom of a hill which gets its
water supply from an open unpressurized
water tank at the top of the hill the
water tank is four meters high and full
and the base of the tank is 50 meters
above the level of the houses faucet
given these distances
what is the houses water pressure as we
just reviewed the pressure difference
between two points within a fluid system
is the density of the fluid times G
times the total difference in height
between those two points so we have the
water pressure in the houses faucet
it's the water pressure at the very top
of the tank which if the tank is open
and unpressurized is equal to
atmospheric pressure this equals 1,000
kilograms per cubic meter times 9.8
meters per second squared times the
total height of 54 meters this is equal
to five point two nine times ten to the
fifth kilograms per meters second
squared plus atmospheric pressure the
units of kilogram per meter second
squared is cumbersome to talk about so
this combination has been defined as its
as its own unit something called the
Pascal after the French mathematician
Pascal whose name has been attached to a
specific physical principle that will be
the subject of a future lesson in
addition this idea of a pressure that is
equal to some number plus atmospheric
pressure gave rise to the concept of
gauge pressure since atmospheric
pressure is essentially equal at both
the top and bottom of this type of
system the gauge pressure in this type
of situation is the total pressure minus
atmospheric pressure when people refer
to the term pressure in most everyday
situations such as discussing their
homes water pressure whether or not they
realize it the gauge pressure is often
to what they are actually referring
that's an introduction to the concept of
hydrostatic pressure the next lesson
we'll review some of its applications in
medicine
you