BIO. The lower end of a long plastic straw is immersed below the ...

Question

BIO. The lower end of a long plastic straw is immersed below the surface of the water in a plastic cup. An average person sucking on the upper end of the straw can pull water into the straw to a vertical height of 1.1 m above the surface of the water in the cup. (a) What is the lowest gauge pressure that the average person can achieve inside his lungs? (b) Explain why your answer in part (a) is negative.

Accepted Answer

Hi everyone today, we are going to determine the least gauge pressure attained inside the person's lungs during the siphoning affluent activity. So the water level in a tall tank is fairly low and a pipe is inserted into the water in the tank. A person will suck on the other end of the pipe, lifting water by only one m above the level of water in the tank. But essentially it does not succeed to make the water flow through the siphon. It can only lift the water by one m. So in this particular problem, we are asked to determine the least gauge pressure attain in this particular problem inside the person's lungs during this activity. So recall that the pressure can actually be calculated using this formula right here. So pressure will equal the atmospheric pressure plus H. Rho G. So the way we want to solve this is first, we want to identify that gauge pressure is actually just identifying the pressure difference or delta P. And the difference will not include the pressure of atmosphere. So Delta P. Is p minus P A T. M. The p here can be substituted with this formula right here. So it's essentially going to be P A. T. M plus H Rho G minus P. T. M. And the P A. T. M will cancel out. So delta P. Is just going to be a church row G. So we want to solve for this particular this particular formula here. Okay, so the pressure of the lungs is equal to the pressure at the top of the liquid in the pipe because we're uh sucking directly from our lungs into the top of the liquid without any difference. So the pressure needs to be smaller than the atmospheric pressure so that the water can actually go up the pipe. So we need the change, so water go up if P which is the pressure instead of the lung is smaller than p of the atmosphere or just on the level or the surface of the water in the tank. So you need be to be smaller than P A. T. M. And therefore in this case we need P minus P. A. T. M. To be negative, just like, So so delta P is equals to, as we have written here will equal to p minus P. A. T. M. And in this case because we know that the p minus B. A. T. F. Is negative. I'm just gonna put a negative sign here. And then this change the p minus P. A. T. M. Or delta P. With h rho G. Just like, so so we know that the H is going to be one m above the level. So this is going to still be minus, this is going to be one m multiplied by the role of water, which is 1000 kg per meter, yup. Multiplied by G. Which is 9.8 m per second squared. And that will be our delta P. Which is going to then be minus 9800 pascal's. Just like, So, okay so now that we found that the least gauge pressure attained is going to be minus 9800 pascal's. We can tackle the second part of this problem which is basically asking why is this negative? So we know that the pressure is negative pressure or the gauge pressure is negative because the P. Has to be smaller than P. A. T. M. And because delta P equals P minus P A. T. M. Then delta P is going to be negative just like so okay, so in this case the pressure inside of the lungs is not going to be zero. Just the difference between the B and the atmospheric pressure needs to be negative so that we can actually suck the water out of the tank and going into the siphon. Okay, so with that we know that the option that is representing our answer here is going to be option A. With the least gauge pressure of minus pascal's and B. Is less than B. A. T. M. Being the reason why the pressure is negative. So I'm just going to write down a here. Okay, so that will be all for this particular problem. Let me know if you guys have any questions or if you guys are still confused, make sure to check out our other lesson video similar to this topic and hopefully you guys will gain a lot more understanding on this topic. Thank you

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