Need help solving an exam question. Thank you

[O'donisR]

Below is a question that I can't understand where the ( .7854) came from.

Question: what is the proximate ampacity of a 2" round bus bar?

solution: Section 366.23 states 1000 A per Squared inch for copper bar

2"x2"=4" x 1000A = 4000A (4000A x .7854 ) = 3141.6 Amps

please I would like some one to explain to me were to take the .7854

Thank you !!

 

[brad9m]

For a round bus bar, you have to use pi*r^2 for the area of the conductor.

The current carried continuously in bare copper bars in sheet metal auxiliary gutters shall not exceed 1.55 amperes/mm2 (1000 amperes/in.2) of cross
section of the conductor.

 

[topham26]

I just learned about this in class actually,

r' = (e^(-1/4)r)

.77880078307 is the number I am talking about but i'm not sure why they use it, it doesn't explicitly describe why it is used in my book

 

[hurk27]

Short cut constant for finding area of a circle

comes from pi/4 (3.1416/4)

So using this short cut you can take .7854*2?"=3.1416sq"*1000=3141.6 amps

 

[hurk27]

I should say there are three ways for finding the area of a circle.

If radii is known pi*r? as pointed out in post 2.

Where diameter in known pi*(d/2)?

And pi*d?/4 which is where the short cut come from by just doing d?*.7854

remember radii is just ? the diameter of a circle so if radii is known just times it by two to get diameter then ? it and times it by the .7854 constant and you have your area which then you can times it by the 1k amps to get the rating of the round buss bar.

 

[gar]

121209-0844 EST

topham26:

In your post what did the equation have to do with the original post. The numeric values are close, but not the same. Define what r' and r are supposed to be. With r = 1 the solution to r' in your equation is the number you provided. But this is not Pi/4.

Your equation may relate to skin effect, but you need to define what it is supposed to represent.

.

 

[K8MHZ]

Below is a question that I can't understand where the ( .7854) came from.

Question: what is the proximate ampacity of a 2" round bus bar?

solution: Section 366.23 states 1000 A per Squared inch for copper bar

2"x2"=4" x 1000A = 4000A (4000A x .7854 ) = 3141.6 Amps

please I would like some one to explain to me were to take the .7854

Thank you !!

Like the others said, it's a short cut, just in the wrong order.

A circle that fits into a 4 square inch square will be less than 4 square inches. It will only be .7854 of the total area.

The math should go: 2"x2" = 4". 4" x .7854 = 3.1416 square inches. So the cross sectional area of the bar would be 3.1416 square inches. That times 1000 amps = 3141.6 amps.

 

[G._S._Ohm]

r' = (e^(-1/4)r)

I've never heard of "e" mentioned in this connection
http://en.wikipedia.org/wiki/E_(mathematical_constant)

 

[handy10]

I just learned about this in class actually,

r' = (e^(-1/4)r)

.77880078307 is the number I am talking about but i'm not sure why they use it, it doesn't explicitly describe why it is used in my book

I believe the equation is a differential equation that is unrelated to the solution of the problem posted. The correct answer is certainly the one given ((pi r^2)/4).

 

[Smart $]

I believe the equation is a differential equation that is unrelated to the solution of the problem posted. The correct answer is certainly the one given ((pi r^2)/4).

You have the equation wrong. It's d?pi/4. The .7854 value is equal to pi/4. So d??.7854.

 

[K8MHZ]

In this particular case, the shortcut is not only longer, but adds some confusion.

Here we have a bar with a radius of 1, so we know that the area of the circle will be 3.1416.

Times 1000 = 3,141.6 amps.

 

[handy10]

You have the equation wrong. It's d?pi/4. The .7854 value is equal to pi/4. So d??.7854.

Thanks. I was trying to find out how to make the formula look right and forgot to look at the symbols. How do you get the 2 to become a superscript?

 

[jim dungar]

How do you get the 2 to become a superscript?

One method is to hold down the ALT key while entering numbers using the numeric keypad (not the ones across the Qwerty keys)

The ones I use most frequently are:
Degree [ALT] 0176 = ?
Squared [ALT] 0178 = ?
Cubed [ALT] 0179 = ?
Micro [ALT] 0181 = ?

 

[K8MHZ]

One method is to hold down the ALT key while entering numbers using the numeric keypad (not the ones across the Qwerty keys)

The ones I use most frequently are:
Degree [ALT] 0176 = ?
Squared [ALT] 0178 = ?
Cubed [ALT] 0179 = ?
Micro [ALT] 0181 = ?

Cool! In fact, cool?

 

[handy10]

One method is to hold down the ALT key while entering numbers using the numeric keypad (not the ones across the Qwerty keys)

The ones I use most frequently are:
Degree [ALT] 0176 = ?
Squared [ALT] 0178 = ?
Cubed [ALT] 0179 = ?
Micro [ALT] 0181 = ?

That is very cool, but how do you do it on a Mac?

 

[jim dungar]

That is very cool, but how do you do it on a Mac?

I don't know, but it seems this guy does.

http://www.georgehernandez.com/h/xComputers/CharacterSets/Shortcuts.asp

 

[jim dungar]

Cool! In fact, cool?

For more, do a web search for ANSI Character Codes (see my previous link).
There are different ways to do this, but many are 'softwar'e depedent. The kyboard method seems to work in the majority of instances.

 

[G._S._Ohm]

That is very cool, but how do you do it on a Mac?

TextEdit, Edit, Special Characters
☛∜∆⁶☚

 

[travish]

Let's see if I got it

Let's see if I got it

3" diameter

3 x 3 = 9
9 x .7854 = 7.0686 sq in?

Is this the same as circle mils?

Travis

 

[Smart $]

3" diameter

3 x 3 = 9
9 x .7854 = 7.0686 sq in?

Is this the same as circle mils?

Travis

Correct and no, respectively.

For circular mils...

3" = 3,000mils
(3,000mils)? = 9,000,000cmils or 9,000kcmils