Measuring Absolute And Gauge Pressure Of Fluids Using U Tube Manometers
In the previous video, we discussed hydrostatic forces. And we applied those principles to a barometer, which is used to measure atmospheric pressure in this video we're going to look at a device called a manometer. And in particular we're going to be looking at YouTube, manometers, we're, also going to relate that to what we've already learned about atmospheric pressure and hydrostatic pressure. So we have two different scenarios here in the first scenario we have a gas in a container.
And that. Containers connected to an u-tube manometer and that's going to enable us to measure the pressure of the gas in that container. We have a similar setup in the second scenario, but as we're going to see in the second scenario, the pressure of the gas is actually less than atmospheric pressure. Whereas in the first scenario, the pressure of the gas is higher than atmospheric pressure. So the first thing that we note from our previous tutorial is the pressure at the same height in a given fluid is going. To be equal. So we know that the pressure at this surface of our liquid must equal the pressure at the same point in the other arm of the u-tube manometer, the pressure in the left-hand arm here represents the pressure of the gas.
And if that pressure is equal to the pressure here, then that pressure is made up of two things it's made up of atmospheric pressure. Because the right-hand arm of the u-tube manometer is open to atmosphere. But we also have a column of liquid here that's going to create. Hydrostatic pressure, let's assume for the purpose of these calculations, the atmospheric pressure is equal to atmospheric pressure at sea level. And we know that that is 101 3 to 5, Pascal's, let's also assume that our fluid is mercury.
And we know that mercury has a density of thirteen thousand, six hundred kilograms per meter cubed. These are some of the facts that we established in the previous video. Now, for this first scenario, let's say that our height of mercury in the right hand, arm of the. Manometer equals 35 centimeters, which is equal to naught point, three, five meters. And what we want to determine is the pressure of the gas we're going to discuss two different types of pressure, we're going to discuss absolute pressure, which is the true value of the pressure of the gas, and we're going to discuss something called gauge pressure, which uses our atmospheric pressure as a datum. And all this will become clear in a moment. Now, if we wanted to determine the absolute pressure of that gas, so.
P absolute, we would need to do atmospheric pressure, plus the hydrostatic pressure caused by the column of mercury. We said that hydrostatic pressure was density times gravity times height. Therefore, the absolute pressure of our gas is 101. 3 2 5, plus 13,600 times gravity, 9.81 times height in meters 0.35, giving us an absolute pressure equal to 1 for 802 1 Pascal's, or we can call that 148 kilo Pascal's.
But if we want to calculate gage pressure, then we're going to need to subtract atmospheric pressure. From our absolute pressure, so we would have 1 4 8 0 - 1 - 101. 3 2 5, giving us a value equal to forty-six point, seven kilopascals. Now, what you may have realized is that we could have simplified that calculation by just doing Rho, G H. Because all we've done is we've added on atmospheric pressure.
And then we've subtracted atmospheric pressure further down, and we'll come onto the reason why that's not always the best approach when we look at our second scenario before we do that is important to. Understand who I gauge pressures are significant, we've calculated the absolute pressure of that gas. So in here at the surface, we know that the absolute pressure is 148 kilo Pascals's. But we wouldn't have a resultant pressure of 148 kilos, Pascal's pushing against that container that wouldn't be the pressure that caused the stress on the outside of the cylinder. And the reason for that is because on the outside, we have atmospheric pressure balancing some of that pressure. So in actual fact we would need.
To use the gage pressure, if we wanted to determine whether that container was going to fail. So we can calculate the absolute pressure of the gas, which could potentially give us more information about its volume and its temperature. But if we're considering whether the container is going to file, then we need to work with our gauge pressures.
Let's take a look at our second example. So in our second example, we know that the pressure at this point in our mercury equals the pressure at this point in. Our mercury so we can see here that atmospheric pressure is actually higher than the pressure of our gas. In the left-hand arm. We have the absolute pressure of the gas, plus the hydrostatic pressure due to the column of mercury.
And on the right-hand side or the right hand. Arm. All we have is atmospheric pressure, let's say for argument's sake that the height. This time is not 0.25 meters. Now, if we want to determine the absolute pressure, then soapy ABS, we can rearrange that formula by subtracting RO.
Gh from each side, and we get P ABS equals P ATM, minus Rho, G H. We can plug in our numbers 101, 3 2 5, minus 13,600 times, 9.81 times 9.25. And that gives us an absolute pressure equal to 68 point 0 kilo Pascals's. But if we want to calculate our gauge pressure in the way that we did that previously was our absolute pressure, minus our atmospheric pressure. So we have 68 kilo Pascals's or the full calculator answer is 67,000, 971 Pascals - 101 3 - 5. Now, what we notice this time then is that we, actually. Have a negative answer - 33.4 killer scales.
And this is the reason why it's not a good idea to calculate gauge pressure using Rho, GH, because if we use Rho, GH, we would have found the gauge pressure to be positive, rather than negative. So if we wanted to determine the temperature of our gas or the volume of our gas, then we would need to use our absolute pressure, that's, the actual pressure of the gas in the container. However, if we want to determine whether this container is going to file, we would. Need to use our gauge pressure because in this instance, we have a pressure pushing outwards equal to 68 kilo Pascals's. But we have a pressure pushing inwards a much larger pressure due to atmosphere of 101 kilopascals or 101 3 to 5 Pascals.
So the net result is that there's going to be a compressive stress on the container in which the gas is contained. Whereas in the previous example, because the gas pressure was higher than atmospheric pressure. The net result was a pressure or a force pushing. Outwards so if we're calculating properties of the gas, we would use absolute pressure under most other circumstances. We would use gauge pressure as atmospheric pressure acts on the outside of our container. And we'd also act on the outside of various other components, such as pressure vessels. You.