In this screencast we are going to calculate

the pressure within a fluid at a certain depth. And we are going to do that through the following

example where we have a water tank that is being used for a large industrial space and

we want to design a level indicator using pressure measurements. So we are trying to

determine whether or not having a pressure measurement system here, we will call this

system 1, makes more sense than having a pressure measurement system labeled 2 shown here. So

we want to determine the pressure at both points of the meter and comment on which location

makes more sense. We are told that the pressure measurement devices are 2 meters long. So

where do we start? We could calculate the pressure and report the pressure as either

a gauge pressure or an absolute pressure. And the big difference between these is that

the absolute pressure takes into consideration the atmospheric pressure in case that is a

factor. Whereas the gauge pressure is 0 when we are reading atmospheric pressure. So let’s

do our calculations first for gauge pressure. Now for systems where we are measuring the

pressure of a fluid and it is not moving. We are actually just measuring the hydrostatic

pressure of that fluid. And we could determine the hydrostatic pressure based on depth. This

is just density times gravity times the height or in this case the depth below the surface.

We could also write this in terms of the specific weight of the fluid, labeled gamma, times

our height. So as you would expect the deeper you go in the fluid, the higher the pressure.

So let’s take a look at our two measurement devices. We are going to label the top as

an A and the bottom as B. So let’s start from the top. If we look at 2A. Pressure measurement

being taken at the top of the surface of the water, we know that at the top of the surface

we just have atmospheric pressure. So our absolute pressure is just atmospheric pressure,

and therefore our gauge pressure is zero. We also know this because if we did use the

calculation our depth is zero. So let’s work in kPa. We will report Pg as 0 kPa for 2A.

Now if we were to measure it at 2B for the same device, this would just be equal to the

density of the fluid times gravity, times depth. And we know that our device is 2 meters

long. We would have to know the density of our fluid, in this case water. And we use

that the density of our water is 1000 kg/m^3. And we know acceleration due to gravity is

9.8 m/s^2. So we plug these two values in and we should get 19600 kg/ms^3 which is the

sam as a N/m^2 or in this case a Pa. So if we were writing it in kPa we would have 19.6

kPa. So now we calculated the pressure at both positions A and B for the second device.

Let’s repeat these calculations for the first device. So if we were to measure the pressure

at the position A for the first measuring device. You might be tempted to think that

because A is being measured at the top of the tank that it is also 0 but that is not

the case. We have all the pressure of the water in the entrance region here that is

on top of this position at A. So even though it is not directly above it, because the water

is not moving, it is stagnant, we have no acceleration, so the pressure here at A, must

also be the pressure at the surface there, and therefore along this level. And so in

this case the gauge pressure is equal to the density times gravity times our depth. In

this case 1.5 m. This should give us a pressure of 14.7 kPa. Now at 2A we can either use the

geometry of the tank, or we know that the device is 2 meters long and therefore repeating

this calculation but using 3.5 meters as our depth below the surface, we get a value of

34.3 kPa. So if we were proposing one of the two positions, which one makes more sense?

Well if we are trying to measure the water level as we use this water level, the problem

with this measurement device, is that 2A will always give us 0 even when the water level

drops. So it is possible that if our water level drops too low below B we won’t get any

readings and we won’t know the level below that position. But one of the positives of

position 2 is maybe we want to make sure there is no overflow in our tank. And if this entrance

region was any higher then we could tell that if the pressure at that position was greater

than 0 then we would have some water level that was above maybe our specifications. And

maybe also we wouldn’t want the water level to drop below position B on the second device

and therefore that could provide a suitable warning. So this fully depends on the specifications

you are looking at and what you are trying to accomplish with that design. So hopefully

this screencast gives you an idea of how to calculate the hydrostatic pressure below a

fluid surface. Here we did it in gauge pressures, we would only have to add the atmospheric

pressures to report these pressures in absolute pressure terms. For more practice visit some

of the interactive screencasts on this topic to test yourselves.

The second 2A should have been 1B.