Conduit Fill question throwing me off

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What size Rigid Polyvinyl Chloride Conduit (PVC), Schedule 40 would be required to install a single 1.5-inch diameter cable?
 
The answer starts in Chapter 9, Table 1, Percent of Cross Section of Conduit and Tubing for Conductors and Cables. For one cable, you may not exceed 53% conduit fill. First calculate the cross-sectional area of the cable with the formula pi x D²/4. So 3.14 x 1.5 x 1.5 / 4 = 1.767in². The divide the area by the maximum percentage fill (53%). 1.767/0.53 = 3.34in². That is your minimum conduit area. On Table 4, the areas of schedule 40 PVC are given. 2" PVC has an internal area of 3.291 in² so it's too small. The next size up is 2-1/2" with an area of 4.695 in². That is your minimum conduit size.

We could have skipped a step and just looked at the one-wire (53%) column of the table after calculating the cross-sectional area of the cable.
 
JoeStillman said:
The answer starts in Chapter 9, Table 1, Percent of Cross Section of Conduit and Tubing for Conductors and Cables. For one cable, you may not exceed 53% conduit fill. First calculate the cross-sectional area of the cable with the formula pi x D²/4. So 3.14 x 1.5 x 1.5 / 4 = 1.767in². The divide the area by the maximum percentage fill (53%). 1.767/0.53 = 3.34in². That is your minimum conduit area. On Table 4, the areas of schedule 40 PVC are given. 2" PVC has an internal area of 3.291 in² so it's too small. The next size up is 2-1/2" with an area of 4.695 in². That is your minimum conduit size.

We could have skipped a step and just looked at the one-wire (53%) column of the table after calculating the cross-sectional area of the cable.
Click to expand...

Joe I get 3.14 x d^2 but where does the divide by 4 come into play
 
Strathead said:
Technically it is the same number of steps.
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Except on my RPN calculator. The X² key is a shift-function and I never use it. It's one less keystroke to do πd²/4.

But the square root function is not a shift, so I never have to enter 1.732, just two keys (3)(SQRT). My old boss saw me do that one time and thought I was dumb and couldn't remember 1.732. Just being lazy, and almost never suffering from fat-finger disease.
 
Strathead said:
Don't feel bad, I struggled as well. I just think Joe is a backwards thinker;). I look at it at D/2=R then R2*3.14=area. Dividing by 4 causes too much thinking.
Click to expand...
Since every term brought pi, and every term brought a division by 4, the constants ultimately cancel out of this calculation.

you can do:
sum(d^2)/D^2

as well as:
sum(r^2)/R^2

and the result will be the same. Note that in my notation here, lowercase letters are the values for the wires, and the uppercase letters are the dimensions of the conduit interior.
 
JoeStillman said:
But the square root function is not a shift, so I never have to enter 1.732, just two keys (3)(SQRT). My old boss saw me do that one time and thought I was dumb and couldn't remember 1.732. Just being lazy, and almost never suffering from fat-finger disease.
Click to expand...
Depending on how you were trained. I prefer keeping irrational constants like sqrt(3) and pi in their original forms, so that they are not the source of rounding errors. It is easier to troubleshoot a calculation seeing the original forms as well. It's no issue when I'm usually using a calculator on the computer anyway.

If I were limited to a 4-function calculator, a cell phone calculator, or had to do it by hand, that's the only time I'd prefer using the approximations.
 
Carultch said:
Depending on how you were trained. I prefer keeping irrational constants like sqrt(3) and pi in their original forms, so that they are not the source of rounding errors. It is easier to troubleshoot a calculation seeing the original forms as well. It's no issue when I'm usually using a calculator on the computer anyway.

If I were limited to a 4-function calculator, a cell phone calculator, or had to do it by hand, that's the only time I'd prefer using the approximations.
Click to expand...
I started doing electrical calculations on slide rules. Other than when taking tests in school, I was hardly ever concerned with much more than 3 significant digits (okay 4 when working with 12.47kV). I bought might first calculator, a Texas Instruments SR50, in 1974 for $128.
 
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jtinge said:
i love those RPN calculators. Still using my HP11 from high school.
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Me, too. I am still using the HP41CV that got me through engineering school 30 years ago. I started out with a TI but I soon learned that the HP with RPN can do complex number calculations internally without me having to do conversions between polar and rectangular coordinates. I remember an exam I took early on which was all complex number chained equations of addition, subtraction, multiplication, and division; the people with the HP calculators were all done in half the time or less than me.

Nowadays when I try to use a calculator with standard notation I have to keep starting over when keying in another number after the "=" clears the register. RPN logic makes sense to me: here's a number, here's another number, multiply them.
 
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