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A U-shaped tube open to the air at both ends contains some mercury. A quantity of water is carefully poured into the left arm of the U-shaped tube until the vertical height of the water column is 15.0 $\mathrm{cm}$ (Figure 13.43$)$ . (a) What is the gauge pressure at the water- mercury interface? (b) Calculate the vertical distance $h$ from the top of the mercury in the right-hand arm of the tube to the top of the water in the left-hand arm.

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a) 1470$P a$ b) 13.90 $\mathrm{cm}$

Physics 101 Mechanics

Chapter 13

Fluid Mechanics

Temperature and Heat

Cornell University

Simon Fraser University

University of Winnipeg

McMaster University

Lectures

03:45

In physics, a fluid is a substance that continually deforms (flows) under an applied shear stress. Fluids are a subset of the phases of matter and include liquids, gases, plasmas and, to some extent, plastic solids.

09:49

A fluid is a substance that continually deforms (flows) under an applied shear stress. Fluids are a subset of the phases of matter and include liquids, gases and plasmas. Fluids display properties such as flow, pressure, and tension, which can be described with a fluid model. For example, liquids form a surface which exerts a force on other objects in contact with it, and is the basis for the forces of capillarity and cohesion. Fluids are a continuum (or "continuous" in some sense) which means that they cannot be strictly separated into separate pieces. However, there are theoretical limits to the divisibility of fluids. Fluids are in contrast to solids, which are able to sustain a shear stress with no tendency to continue deforming.

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Okay, so this problem we have a u shaped to. So the first of all this drought it to being here. So this is to and we have interface between America three and water. So first of all, that's what Here, do you water? And here we have the American re. So this is the mercury far I see all decided here have Merrick Ary. Okay, so, first of all, the first thing we need to calculate, uh, we know that this is age here. We have 15 ST Emitters, and here we have a judge the difference between their heights. So the first thing we need to calculate is what is the pressure in the interface between May Khoury and Water? So we want to calculate the pressure on this point, and here, therefore, we just need to use the equation for pressure. So the pressure in that point is going to be That's put in here pressure going to be, uh, ho, which is the density off the water. G age. So that's the pressure. In that point, we can consider the humus fired, give pressure. But since the problem once engaged, pressure the gauge pressure is the difference between pressuring that point. We have beaten atmospheric pressure So that iss the gauge pressure. So this is just hope The density of the water. G h that's the Cray, the equation that we need to solve. Okay, so let's complete this. We have that the gauge pressure is going to be 1000 which is the density of the water. The multiplies gravity acceleration of 9.8. They're multiplies 15 or actually, we went in meters. So this is going to be zero point 15 meters. So calculating this we have a pressure off one point 47 times 10. 33 Asko. So that's the answer to the first item on the second night. And the second thing we need to calculate is the height off the right are off the U shaped tube. So we want to calculate the value off age. Okay, And how are we going to manage to do this? Well, we know that the pressure on this point should be equal The pressure on the water Makary interface. Therefore, we can see that this pressure here, which is just what's put in here This pressure here is going to be Let's see hope off mercury that multiplies G the multiplies X, because this size here is on Lee X. Okay, So let's calculate what is the value off acts? Because we know that pressure should be equal so we can see that X is going to be equal. One point 47 times 10 to the tree divided by the density of mercury reaches 13 0.6 Time Stan to victory. They're multiplies the gravity, the separation, which is nine point eight. So if we calculate this, we get that the X is just 1.1 same team enters, and if we look to the draw, we can see that age plus X is going to be equal 15. Therefore, we can say that the age that we want to comfortably is just 15 miners X, which gives us a total off 13 0.9 same team mentors. And that's defined. Arrested. Just problem. Thanks for

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