Amount in Feet

[Guest]

A cu. in. of lead weighs 2/3 lbs. Determine feet of lead pipe which can be produced from 100 lbs. of lead, the diameter 3/4 in. and thickness 1/8 in.

Check my calculations:

Let L = length of pipe.

3.1416 x 0.4375 x 0.4375 = 0.60132 sq. in. (area)

3.1416 x 0.4375 x 0.4375 x L = 100

0.60132L x 0.6666 = 0.4008L cu. in. (volume)

0.4008L / 0.4008 = 100 / 0.4008

L = 249.475 = 249 ft.

[Guest]

Is pipe 3/4 in. ...... O.D or I.D

[Guest]

3/4 is I.D.

[Guest]

If we take 3/4 = ID then "r" = 3/8 and "R" = 0.5 and "D" = 1 and thickness "t" = 1/8

Area of pipe crossection "A" = Pi(R^2 - r^2) = Pi(R + r)(R - r) = Pi(D - t)(t) = Pi(7/8)(1/8) = Pi(7/64)

So Area = = 7*Pi/64

100 lbs of lead has volume of 100*3/2 = 150 cu ins.

length = V/A = 150*64/(7*Pi) = 436.5 ins. OR 36ft 4.5 ins.

[Guest]

" If we take 3/4 = ID then "r" = 3/8 and "R" = 0.5 and "D" = 1 and thickness "t" = 1/8 "

" Area of pipe crossection "A" = Pi(R^2 - r^2) = Pi(R + r)(R - r) = Pi(D - t)(t) = Pi(7/8)(1/8) = Pi(7/64) "

I am not totally clear on these steps.

[Guest]

" If we take 3/4 = ID then "r" = 3/8 and "R" = 0.5 and "D" = 1 and thickness "t" = 1/8 "
This is self explanatory......If 3/4 is ID inside diameter then inside radius "r" must be 3/8.
If ID is 3/4 and thickness is 1/8 then Outside Radius must be 3/8 + 1/8 = 4/8 = 1/2 or 0.5. That make OD outside diameter = 1

" Area of pipe crossection "A" = Pi(R^2 - r^2) = Pi(R + r)(R - r) = Pi(D - t)(t) = Pi(7/8)(1/8) = Pi(7/64) "
Similarily this is the various form for the area of an annulus or area between 2 concentric circles as in the crossection of a pipe.
Area = Pi(R^2 - r^2) this is Pi times big R squared minus little r squared. = pi[(1/2)^2 - (3/8)^2] = pi[1/4 - 9/64] = pi [16/64 - 9/64] = pi[7/64] = 7*pi/64.

OR in the other form using the fact that the difference of 2 squares is their sum times their difference
Area = Pi[(R + r)(R - r)] = Pi[(1/2 + 3/8)(1/2 - 3/8)] = Pi[(7/8)*(1/8)] = Pi[7/64] = 7*Pi/64.

OR in the other form noting that (R + r) = (D - t) .....the outside diameter minus the thickness......and....(R - r) is just the thickness.
Area = Pi[(D - t)(t)] = Pi(D - t)(t) = Pi*[1 - (1/8)]*[1/8] = Pi[7/8][1/8] = Pi[7/64] = 7*Pi/64

[Guest]

Area = 7*Pi/64
It is usual in some instances to take PI as 22/7 instead of the usual 3.1416.
So Area = 7*(22/7)/64 ......the 7s cancel leaving Area = 22/64 = 11/32
So Area = 11/32

So Area = 11/32

100 lbs of lead has volume of 100*3/2 = 150 cu ins.

length = V/A = 150*32/11 = 4800/11 = 436.36 ins. = 36 feet 4.36 inches.

[Guest]

Thanks again.