What does the top pressure gauge read in FIGURE EX14.28?

Video transcript

Welcome back, everyone. We are making observations about this system of pressure gauges and pipes here. Now, I'm gonna label this bottom pressure gauge gauge one and this top pressure gauge gauge two. And we are tasked with finding what is the reading on our bottom pressure gauge. Now, before we get started, I do wish to acknowledge the multiple choice answers here. On the left hand side of the screen, those are going to be the values that we strive for. So without further ado let us begin. Well, since we have water flowing through these pipes, we can consider water to be an ideal fluid. So we can apply Bernoulli's equation which states the following that the pressure in pressure gauge one plus one half times the density of water times the velocity at pressure gauge one squared plus the density of water times the acceleration due to gravity times the height of pressure gauge. One is equal to P two plus one half row V two squared plus row G. Why? Who now what I'm gonna do is I'm going to subtract this entire term on the left-hand side of the equation from both sides. And what we get is P one is equal to P two plus and I can take one half row out of a lot of these terms, I can get one half row times V two squared minus B one squared plus row G times Y two minus Y one. We have all of these values present in our image. So let's go ahead and calculate P one, P one is equal to, well, the pressure of pressure gauge two, which is 125 kilo pascals, but we need it in Pascal. So this is 1 25 times 10 to the third pascals plus one half times the density of water, which is just 1000 and times V two velocity at gauge two, which is 1.5 squared minus one squared plus 1000 times 9.81 times the height of pressure gauge two, which is two minus the height of pressure gauge one which is zero, plugging all of this into our calculator. What we get is 145 times 10 to the third pascals or 145 kg pascals corresponding to our final answer. Choice of C Thank you all so much for watching. I hope this video helped. We will see you all in the next one.