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Expert: - 3/28/2011


Question
An old inclined sewer pipe has silted up and is to be renewed.
It runs south at a bearing of 180° for a horizontal distance of 140.5 m and rises at a steady gradient to a vertical height of 3.45 m.
The sewer then turns and heads off at a bearing of 120° for a further horizontal distance of 74.8 m and rises another 1.75 m. This entire sewer is to be replaced by a new straight section of pipe.

(1)Find the length of the old sewer and hence the volume of silted-up material.
(2)Calculate the length of the new straight replacement sewer pipe in metres and show this clearly on your diagram.
(3) What approximations and limitation are linked to the solutions you produced in question 2.

Answer
The current length of the 1st pipe is 140.54' and the 2nd pipe is 74.82'.
The total length is 215.36'.

Since the 2nd pipe bears off of the first pipe by 60°, that means it goes half of its lenth to the south and √3/2 of its distance at a right angle.  This makes it go 177.95 to the south
and 64.80 feet at a right angle.

What we have is a box, and the numbers I just gave were the length and width.
The last measurement is the height, and that is 3.45 + 1.75 = 5.2.

To find the actual length needed, it is √(177.95² + 64.80² + 5.2²) = 189.45'.

(1) The volume is the cross-sectional area of the pipe times the length,
but I can't see where the radius of the pipe is mentioned.
All I got was the total length was 215.36'.

(2) The length of the new pipe is 189.45'.
That is the diagonal in 3-dimensions connect one corner to the opposite corner.

(3) The new pipe may probably won't fit on the ground without some digging or filling in required to make it run level from the start to the end.  

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Scott A Wilson

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I can answer any question in general math, arithetic, discret math, algebra, box problems, geometry, filling a tank with water, trigonometry, pre-calculus, linear algebra, complex mathematics, probability, statistics, and most of anything else that relates to math. I can even tell you it takes me over 2,000 steps to go a mile, but is that relevant?

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