BIO In intravenous feeding, a needle is inserted in a vein in the patient's arm and a tube leads from the needle to a reservoir of fluid (density 1050 kg/m^3) located at height h above the arm. The top of the reservoir is open to the air. If the gauge pressure inside the vein is 5980 Pa, what is the minimum value of h that allows fluid to enter the vein? Assume the needle diameter is large enough that you can ignore the viscosity of the liquid.

Video transcript

Hi everyone in this problem. We will have a waterline engineer who wish to add fertilizer solution to a pipeline and we will have a gauge pressure off the water flowing in a pipe of 17.5 kg pascals. And the fertilizer solution will have a density of 10 20 kg per meter cube which is placed in the tank. We are asked to actually determine the least height off the tank above the pipeline that will still drive this uh the fertilizer solution to a connecting host into the pipe. So first, we want to recall that pressure can be calculated by um sum uh summing the atmospheric pressure of P ATM plus the effect of the depth which is each row G. And then we wanna also recall that gauge pressure is essentially just the pressure difference which will be the pressure minus the atmospheric pressure where this pressure right here will be coming from our formula there. So substituting that this will be P ATM plus H row G minus P ATM and the P ATM will cancel out. So delta P or gauge pressure where will just essentially be H multiplied by row multiplied by G, just like that. From this uh uh problem statement, we know that delta P or the gauge pressure is 17.5 kg pascals, which is essentially just 17.5 times 10 to the power of three pascals. And then we also know that the row is 20 uh 10 20 kg per meter cube. And those two information are what's needed for us to actually calculate the least height of the tank. So we're gonna substitute that into this formula right here. So the delta pure gauge pressure is 17.5 times 10 to the power of three pascals. And the height is the ones that's being asked. The row is 10 20 kg per meter cube and the G is normal which is 9.8 m per second squared. Then we will determine the height to actually be 1.75 m. So 1.75 m is actually going to be the answer to this problem which will correspond to option B. So option B is going to be our answer choice and that'll be all for this particular practice video. If you guys have any sort of confusion, please make sure to check out our similar videos on this particular topic and that'll be all for this one. Thank you.