ADVANCED SOLID WASTE MANAGEMENT UNIT IV

This requires us to understand a formula. Terminal velocity empirical equation, which you can also review on pages 203-204. So, our facility has purchased an air classification system with a fan that can generate an air flow rate in the system that goes up to 20 feet per second. Your hammermill shredder is able to provide a waste stream containing plastic that passes a three centimeter grate, if the density of the plastic is 0.875 grams per centimeter. The facility does not have the means to conduct a drop test, but as the site consultant, they want you to make your best estimate if the unit will separate out the plastic from the shredded waste. So that’s why we will use the terminal velocity empirical equation. And “Vs” is the velocity, the settling velocity, and it’s in feet per second units. The 1.9 is a constant as is the 0.092. The, I want to call this rho, it looks like a “P” but it’s Greek symbol rho, is the particle density in units of pounds per cubic feet. Anytime you see rho, you’re going to know that it’s talking about density. But anyway, so you’re literally going to take this constant, .092, and multiply it by whatever we figure out the particle density in units are. Then, the “A” is the particle area, usually in length times width and units of inches squared. So, you will take whatever you calculate “A” to be and you multiple it by 5.8. So, you’re literally going to multiply these two values together, multiple these two values together, and then add across. Okay? So the first thing we want to do is go ahead and calculate the particle density, and we have the particle density in terms of grams per centimeters and we need them in terms of pounds per feet, so that’s why we have this conversion going on here. So, we have our grams per cubic meter, and notice this, I got my cubic meter here, but notice this right here just says centimeter, but you have to cube the whole answer, so you’re literally doing 2.54 cubed, so you might want to calculate this first. And write the answer down. The same with this. This is 12 inches and we need it to be cubic feet. So, 12 inches is a foot, but we have to convert it to cube, so that’s why it’s to the third power. Now, notice that the grams go away. The inches go away. The centimeters go away, the units, and what are we left with? Pounds per feet, and it’s cubic feet because when you do this three times, it will make this a cube. So, literally what you’re doing is taking .875, multiplying it by the answer to this, 2.54 cubed, and then 12 cubed. Okay, then you’re going to divide it by 454 to get 54.6 pounds per cubic feet. So, that’s what our particle density is. That’s going to be multiplied to this .092. Okay? Now, let’s go ahead and calculate “A,” and “A” is going to be in units of inches squared. We started with 3 centimeter grate. So it’s three times three. Why? Because it’s length times width. So, we do 3 centimeters times 3 centimeters and then here’s our conversion, 2.54. Notice you have to do the whole thing, so it would be 1 divided by 2.54, and then square that answer. Okay? And that’s how you get that 1.4 inches squared and notice the centimeters go away. There’s 2 centimeters here; there’s 2 here. Remember, this becomes squared because of that. So you’re literally taking nine, three time three is nine, and you divide it by 2.54 squared, and you get 1.54 inches squared. Now, we have the numbers needed. We have our 54.6, and we have our 1.4. And then you just plug it into the formula, so I would multiply this first, then multiply this first, add them together then add the 1.9, and you get 15.04 feet per second. Now, what does it say up here? As long as it is less than this flow rate of 20 feet per second, and 15.04 is, so this means the unit will separate the plastic from the shredded refuse.