A pressure difference of 6.00 * 104 Pa is required to maintain a volume flow rate of 0.800m3/s for a viscous fluid flowing through a section of cylindrical pipe that has radius 0.210 m. What pressure difference is required to maintain the same volume flow rate if the radius of the pipe is decreased to 0.0700 m?

Video transcript

Welcome back everybody. We are looking at some oil pumps here. Let me go ahead and draw them out. We have that. An oil pump maintains a volume flow rate through a given pipe. This is our old pipe that we're dealing with. Right? We are told that it has a diameter of D. A volume flow rate which I will mark as V. O. For old pipe flow rate and a pressure difference given by delta P. Not write a difference in pressure. So pressure difference. Right now I keep saying old because this pipe is going to be replaced now this pipe is going to be replaced with a new pipe that has a diameter. Let me draw that a little bit better here. That'll work. Now we're told that the diameter is half of the original pipes diameter. Now we need to maintain the original flow rate but we are tasked with finding what this new delta P should be or what a ratio for the new delta P should be. Well, when we are dealing with low rates through a pipe, we know that the pressure difference. Now this is for this is our old original pipe here. Our pressure difference is going to be proportional to the length of the pipe, over the radius to the fourth power. Right, so looking at our new pipe here, let's apply that formula or the proportionality to our new pipe. We have that our new delta P is proportional to the length of pipe. We know that the length is going to be the same times the radius of our new pipe to the fourth. Well, if the diameter is half of the original diameter, that means the radius of our new pipe will be half of the original radius. Right? So solving for this, we actually get that this is two to the fourth times the length over our to the four, but L over R. To the fourth is just our original delta P. This means that our delta P. New is proportional to 16 times our original pressure difference or responding to our answer choice of D. Thank you all so much for watching. Hope this video helped. We will see you all in the next one.