19. Fluid Mechanics
Pressure Gauge: Manometer
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Everybody. Hopefully, you try this practice problem here. So we've got a classic manometer. It's got one of the ends that's open, so we got, some kind of, atmospheric pressure on the left side, and we've got 2 atmosphere gas on the other. Now we're gonna fill this thing with mercury. So remember that mercury here, this is h g. Remember that the density of mercury is equal to 13,600. You might wanna just memorize that. It's really important. We're gonna measure the top of the mercury column on the left to be 40 centimeters higher than on the right. So basically, what that means here, remember, is that on the left side, it's gonna touch that atmospheric pressure on the left. On the right side, it's gonna be the boundary between the two atmosphere gas. You always draw the straight across over here and this height difference, this h is gonna be 0.4. That's gonna be 40 centimeters. Now, we're gonna calculate the atmospheric pressure in atmospheres that the manometer is exposed to. So what does that mean? We've got 2 atmospheres on the bulb side, On the left side, it's open, presumably to the air that's on the outside here. Now what you might be thinking is that isn't this atmospheric pressure just 1? And no, it's not. Remember that if they say standard atmospheric pressure, then that's always 1 ATM. But if you're ever asked to calculate the atmospheric pressure, then you cannot assume that it's 1 atmosphere. Right? Remember that pressure changes, like if you were to go up a mountain or something like that. Right? So you could have this instrument somewhere that isn't at standard atmospheric pressure, and this is actually what we wanna calculate here. Okay? So whenever you ask for it, you can't just assume it's 1. So how do we do this? Well, remember, we're just gonna use our P bottom equation. So you've got P bottom equals P top plus row g h. Alright? So we got the density of the liquid, we've got the height of the column and g is just a constant. So So now what about the top and the bottom pressures? Well, P top remember is always at the top of the column here. So basically, that's what we want to calculate. What is the P top? That's really what we want to find here. The bottom is gonna be the, the pressure of whatever the the bulb pressure is. Right? The bottom is basically gonna be the same pressure as this, and this is just gonna be the same pressure as whatever the gas is. So in other words, this p bottom here is just p gas and the p top here is gonna be the p atmospheric pressure. That's really what we really want. So this is gonna be a plus. Now we've got 13,600, times 9.8 times 0.4. Remember that p gas here is really just equal to, 2 atmospheres. Remember, we can't plug in 2 atmospheres. We have this. We have to convert this to pascals. Remember that the conversion is that 1 atmosphere is equal to a 101,000 pascals. So if 1 atmosphere is 101,000, then 2 atmospheres is equal to 202,000 Pascals. This is gonna be, ATM. And then what happens is you're gonna get this is patm e, plus. And then when you work this out, what you get here is 53,312 Pascals. So now I just move this over, and what you're gonna get here is that p atmosphere is equal to, 149,000 pascals. Alright? Just writing it to the nearest sort of 1,000 here, but that is your answer. But we actually want this we wanna calculate this in, atmospheres. So now we all we all we have to do is we just have to use this conversion factor again. So we're just gonna use, this is gonna be divided by we're gonna have 1 atmosphere here. We're gonna divide by a 101,000 pascals to get rid of pascals, and we're gonna get atmospheres and what you should get is 1.47 atmospheres. Alright? Now, it makes sense that we got a number that was less than 2. And the reason for that is this is 2 atmospheres on the right side and this atmospheric pressure on the outside is gonna be 1.47. It makes sense that it's less because that means that the 2 atmosphere on the right side is gonna push down more in the column than on the left side, and so it's naturally gonna go up like this. Okay? So that totally makes sense we got something that was less than 2. Alright, folks. That's it for this one. Let me know if you have any questions.
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