Let’s take an example where we get to find something about this pressure. In this case,
we assume you’re diving 10 meters under water. We could ask how much gauge pressure
do you feel just from the water. How much total pressure do you feel if we include the pressure
just from the atmosphere? Then how much will this change if you dove down even deeper to 20 meters?
If you’re now diving 10 meters under a pool with twice the surface area, so we haven’t changed
anything about the problem but just increased the surface area of the pool, we could also ask
how much pressure you would feel in that situation. So, give this a try using the equations
for pressure, the atmospheric and the gauge pressure that we’ve just introduced
and see if you can do it. If you do, so it should look something like what we’re about to show here.
So, if you did this problem, hopefully, your analysis looks something like this. We’re first going to find
the gauge pressure on our person who’s swimming under water. We just saw that this is equal
to the density of the fluid, in this case water times g times the height or the distance below the water
that they went. We’ll use our SI units, the standard units for the density of water
which is 1000 kilograms per cubic meter. G, we can approximate as 10 again just for solving these problems
very quickly and finding answers especially in an exam. Then we say that they went 10 meters under water.
So, we have three 1's with one, two, three, four, five zeroes. So, using our scientific notation,
this is 10 to the 5th newtons per meter squared which fortunately is our unit for pressure.
So, this 10 to the 5th pascals or writing it in terms of kilopascals as we’ve seen, we can write this as
10 squared kilopascals or 100 kilopascals. So, everything that I’ve just written here are just
different ways of writing the same thing. The reason that I’ve written this in so many different ways
is that in the exam setting, many times when you’re looking for a particular answer to a problem
that you’re solving, especially when we get to fluids, when we don’t always use our SI unit
our standard units, we might see it written in many different ways, in pascals, in scientific notation
or not in scientific notation. So, be careful if you’ve arrived at some sort of solution
and if you see something that doesn’t quite match with the solution that you’ve written down,
not to panic. Just sort of look through and see if it might be compatible with the solution
that you wrote just by rewriting it. So, continuing this problem, we’ve also got the question
about what happens if we want to find the total pressure. Remember that this is equal to
the atmospheric pressure plus the pressure that they’re feeling from the water, in this case
the gauge pressure that we just found. The atmospheric pressure, we already mentioned is about
100 kilopascals. It turns out this is exactly the same as the pressure that we just found
in our example, also 100 kilopascals. So, this is simply equal to 200 kilopascals.
The final thing that we need to do now is ask what happens if we change the depth
and go down to 20 meters deep. What that will do is change this number in particular right here.
Remember, this depended on the height, the depth that you went to. So, if we double this depth,
although what happens is this number will double to be let’s say if we go down to 20 meters,
200 kilopascals of pressure just from the water. But remember that this does not change
our atmospheric pressure. So the total pressure, so that’s right, this is the gauge pressure
at 20 meters. Now, if we want to find the total pressure when you’re at 20 meters deep,
you would again add the pressure that you found from the gauge pressure, the water above you
plus the pressure from the atmosphere. So adding these together, atmospheric plus P gauge
at 20 meters, we now instead have 100 kilopascals plus this quantity here which is 200 kilopascals.
Now, we have 300 kilopascals of pressure in total when you dive down to 20 meters of depth.