A hurricane wind blows across a 6.0 m x 15.0 m flat roof at a speed of 130 km/h.(b) What is the pressure difference?

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Hey, everyone in this problem, we are told that on the top of a hermetically sealed plexiglass cube with a side length of 15 centimeters, a hair dryer blows air of density 1.6 kg per cubic meter at a speed of 50.0 m per second. Were asked to calculate the pressure difference delta P between the inside and outside of the cube. And we are given four multiple choice options. Option A zero pascals, option B 106 pascals, option C 1.3 kg pascals and option D 2.5 kg pascals. So the first thing I'm going to do is kind of draw AAA kind of a sketch of what's going on here. So here is a crude drawing of one face of the plexiglas cube. And we're told that the cube is hermetically sealed, which means it's air tight. So none of the air is coming through. But we're also told that a hair dryer is blowing air nearby. So we'll say that uh just above the cube, there is just around the cube, there is air blowing at a speed of V now because we're looking for a pressure difference based on some speed difference between the inside and outside of the cube. This is going to be a case where we will want to use the Bernoulli equation because the Bernoulli equation gives us a relationship that involves pressure and, and the flow of speed. And so according to the Bernoulli equation, the quantity p pressure plus one half multiplied by the density row V squared plus row multiplied by the gravitational acceleration multiplied by the Y position of the flow is constant. So everything on the left hand side of this equation I've written is going to be the same. We use the Bernoulli equation to compare two different parts of a flow or a section of flow. So I'm going to add similar labels to this diagram. I'm going to label the 20.1 as the point inside the cube just underneath the top surface of it. And then I'm going to use the subscript two to refer to the point just above the cube surface on just on the outside of it. So P sub one plus one half row V squared V one squared plus row G Y one is equal to P two plus one half row V two squared plus row G Y two. And that's the Bernoulli equation for this problem. Now, let's get to work simplifying this a bit because I've defined points one and two to be basically right next to each other. We can assume that Y one the position of the flow 10.1 is approximately equal to Y sub two, the flow position of 20.2, which means that the gravitational potential energy terms row G Y one and row G Y two are approximately equal. And as a result will cancel out the other way I'm going to simplify. This is by noting that since the cube is hermetically sealed, and we're not told anything about there being a net flow inside the cube, we can assume that V sub one is approximately zero, which means that the one half row of the one squared term also goes to zero. So a much more simplified version of this equation tells us that the pressure at 0. is equal to P two plus one half row V two squared. So now we've simplified the equation quite a bit. Since the problem is asking for the pressure difference, I'm going to subtract it from both sides of the equation P sub two so that we can get P sub one minus P sub two, a pressure difference on its own. And this is equal to one half multiplied by row V sub two squared. So that means that this small little term here is going to be the answer to the problem. So let's just plug in the variables that we have. This is one half multiplied by the density row, which was given to us in the problem as 1. kg per cubic meter. And then for V two, that's given to us in the problem as 50 m per second. So 50 0.0 m per second and the whole term is squared. So now all we gotta do is put this into a calculator. And if we do that, then we find a pressure difference of about 1325 pascals or writing this in scientific notation, converting it from pascals to Helo Pascals, it's about equal to 1.3 pacos. And that is then the answer to the problem. We're asked to find the pressure difference. So this is the solution. And if we look above at our multiple choice options, we can see that option C does indeed say 1.3 kg pascals. So that must be the answer to this problem. And that's it for now. I hope this video helped you out. If you would like to see more, please check out some of our other videos and hopefully they will give you more practice with these types of problems, but that's all for this video. And I hope you have a lovely day. Bye bye.

A hurricane wind blows across a 6.0 m x 15.0 m flat roof at a speed of 130 km/h.(b) What is the pressure difference?

Verified Solution

Key Concepts

Bernoulli's Principle

Pressure Difference

Conversion of Units