CHAPTER 3. GENERAL CONSIDERATIONS FOR PRESERVATION OF FRUITS AND VEGETABLES
Explore pressure in the atmosphere and underwater. Reshape a pipe to see how it changes fluid flow speed. Experiment with a leaky water tower to see how the. The bottle will have a small hole where water will flow out. The graduated the hole increases? What happens to the flow rate when pressure is applied to the bottle? Organize your data into a chart and graph your results. . Lesson Plans · Worksheet Generator · Common Core Resources · More Teaching Tools · Schools. A graphic showing flow through a nozzle with the mass flow rate equation for The conservation of mass (continuity) tells us that the mass flow rate through a tube is a Button to Display Grade Activity Button to Display Grade Activity.
It would have traveled-- let's assume that the pipe doesn't change too much in diameter or in radius from here to here.
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It would have traveled velocity times time, so V in times time. It could be meters or whatever our length units are. After T seconds, essentially this much water has traveled into the pipe. You could imagine a cylinder of water here. Once again, I know I made it look like it's getting wider the whole time, but let's assume that its width doesn't change that much over the T seconds or whatever units of time we're looking at.
What is the volume of this cylinder of water?
The volume-in over the T seconds is equal to the area, or the left-hand side of the cylinder. Let me draw the cylinder in a more vibrant color so you can figure out the volume. So it equals this side, the left side of the cylinder, the input area times the length of the cylinder.Calculating Pressure and Flow
That's the velocity of the fluid times the time that we're measuring, times the input velocity times time. That's the amount of volume that came in. If that volume came into the pipe-- once again, we learned several videos ago that the definition of a liquid is a fluid that's incompressible. It's not like no fluid could come out of the pipe and all of the fluid just gets squeezed. The same volume of fluid would have to come out of the pipe, so that must equal the volume out.
Whatever comes into the pipe has to equal the volume coming out of the pipe. One assumption we're assuming in this fraction of time that we're dealing with is also that there's no friction in this liquid or in this fluid, that it actually is not turbulent and it's not viscous.
A viscous fluid is really just something that has a lot of friction with itself and that it won't just naturally move without any resistance. When something is not viscous and has no resistance with itself and moves really without any turbulence, that's called laminar flow.
That's just a good word to know about and it's the opposite of viscous flow. Different things have different viscosities, and we'll probably do more on that.
Like syrup or peanut butter has a very, very high viscosity. Even glass actually is a fluid with a very, very high viscosity. I think there's some kinds of compounds and magnetic fields that you could create that have perfect laminar flow, but this is kind of a perfect situation.
In these circumstances, the volume in, because the fluid can't be compressed, it's incompressible, has to equal the volume out. What's the volume out over that period of time? Similarly, we could draw this bigger cylinder-- that's the area out-- and after T seconds, how much water has come out? Whatever water was here at the beginning of our time period will have come out and we can imagine the cylinder here.
What is the width of the cylinder? What's going to be the velocity that the liquid is coming out on the right-hand side? Capital V is volume, and lowercase v is for velocity, so it's going to be the output velocity-- that's a lowercase v-- times the same time.
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So what is the volume that has come out in our time T? It's just going to be this area times this width, so the output volume over that same period of time is equal to the output area of this pipe times the output velocity times time. Once again, I know I keep saying this, but this is kind of the big ah-hah moment, is in that amount of time, the volume in this cylinder has to equal the volume in this cylinder.
Maybe it's not as wide, or something like that, but their volumes are the same. You can't get more water here all of a sudden than what's going in, and likewise, you can't put more water into the left side than what's coming out of the right side, because it's incompressible These two volumes equal each other, so we know the area of the opening onto to the left hand of the pipe times the input velocity times the duration of time we're talking about is equal to the output area times the output velocity times the duration of time we're talking about.
It's the same time on both sides of this equation, so we could say that the input area times the input velocity is equal to the output area times the output velocity.
This is actually called in fluid motion the equation of continuity, and it leads to some interesting things. For all solvents at higher concentrations, this gives rise to complex osmotic behavior with far greater than expected from van't Hoff equation osmotic pressures that depend on the degree of polymerization and the interaction between the chains. Polymer chains have random configurations sweeping through space and occupying much larger volumes than the molecular partial volume.
The polymers effectively remove screen some of the solvent from the solution by reducing the 'free' volume of solvent available. The osmotic pressure of pullulan from [ ] As the concentration of the neutral polymers increases, an overlap between the chains increases with increasing contacts between the monomers and the solution is no longer homogenous.
The osmotic behavior of branched polymers is complicated by the degree and order of the branching with the osmotic pressure dependent on the 'free' volume of solvent available. When the solvent is water, there are two ways that water becomes bound i. As there is likely to be overlap between these effects they may well be only partially or insignificantly additive.
Volume flow rate and equation of continuity
As above, the osmotic behavior of polyelectrolytes in water depends on the mass concentration relative to that concentration at which the molecules overlap in solution [ ]. Polyelectrolyte gels are may swell to a much greater extent e.
The elasticity of the gel counteracts this by exerting pressure on the contained water. Shows the area that polymers cannot penetrate A different effect occurs in suspensions of inert particles in polymer solutions. It is found that such particles do not exert any osmotic pressure.