Video Transcript
What is the pressure exerted by
water at a depth of 2.5 meters? Use a value of 1000 kilograms per
cubic meter for the density of water.
So in this example, say that we
have a column of water. And we’re interested in the
pressure exerted by that water at a depth of 2.5 meters below the surface. So let’s say that’s a point here in
our water column. The pressure at this point we’ve
marked is created by the weight of all the water that’s above that point in our
water column. And by the way, it doesn’t make a
difference how wide the column is. However wide or narrow it is, the
pressure will be the same as long as we have this certain depth, 2.5 meters.
To answer this question of what is
the pressure exerted by the water at that point, we can recall that the pressure
created by a fluid is equal to the density of that fluid multiplied by its height
below the surface of the fluid times 𝑔, the acceleration due to gravity. Recalling that 𝑔 is 9.8 meters per
second squared, when it comes to the density of our fluid, we’re given that in our
problem statement, 1000 kilograms per cubic meter. And we’re also given the height, ℎ,
2.5 meters. And this means we can get right to
calculating this pressure. It’s equal to the density of the
water multiplied by the height below the surface of the water times the acceleration
due to gravity.
Now before we multiply these
numbers together, notice the units involved. That all the units are in base unit
form. We see that in the numerator of our
units, we have these two factors of 𝑚, the distance in meters. While in the denominator, we have
meters cubed. This means if we were to multiply
all the units involved together, we would get an overall result of kilograms per
meter second squared. This is equivalent to a newton per
meter squared. And we can recall that a newton per
meter squared is equal to the unit pascal, which is a pressure unit. This means that the units we’ll end
up with after we do our calculation are pascals. When we multiply these three
numbers together, we find a result of 24500 pascals. That’s the pressure exerted by the
water at this depth.
