Rise of an arc: 8-ft pipe, ends at A, B, center at C, ground is D. How far will C rise from D if...?

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BrunMar

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In need to know the rise of an arc. If that's what you call it.
I have an 8 foot pipe. If point A is one end and point B the other, with point C being the center of the pipe and D being the ground. How far will point C rise from point D if point B is pushed 2 feet closer to point A. Wouldn't point C simply rise 2 feet? No, because if I would push A all the way to B (8ft), that would bend the pipe perfectly in half putting C only 4 feet from D.
Ok, so then, I have a 6 foot span i wish this pipe to arch over. How long would the pipe need to be if I wanted point C to be 18in from point D, with A & B obviously being on opposite ends of the span.
 
BrunMar said:
the rise of an arc. If that's what you call it.
Click to expand...
Hi BrunMar. In math, an arc is part of a circle (i.e., a segment of the circumference).

I think the curve of your pipe (circular, elliptical, parabolic, catenary, etc) depends on its material and thickness. Even if the pipe's curve were circular, we would need to know the radius.

Do you have any more information?

:)
 
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BrunMar said:
In need to know the rise of an arc. If that's what you call it.
I have an 8 foot pipe. If point A is one end and point B the other, with point C being the center of the pipe and D being the ground. How far will point C rise from point D if point B is pushed 2 feet closer to point A. Wouldn't point C simply rise 2 feet? No, because if I would push A all the way to B (8ft), that would bend the pipe perfectly in half putting C only 4 feet from D.
Ok, so then, I have a 6 foot span i wish this pipe to arch over. How long would the pipe need to be if I wanted point C to be 18in from point D, with A & B obviously being on opposite ends of the span.
Click to expand...
Hi @BrunMar

You appear to be asking two different questions here!

(Assuming that in both cases the start point (A) of your pipe is at ground level, ie: Point D)

In the first instance you say you have an 8 foot long pipe that you wish to curve (in a circular path) such that its end point (B) is 6 feet (horizontally) away from its start point (A) and its midpoint (C) will be 18" above the ground (ie: Point D).
(I suspect that simply may not be possible. 🤔)

Then, later, you appear to change the question to: How long will a pipe be if it is curved (in a circular path) such that its end point (B) is 6 feet (horizontally) away from its start point (A) and its midpoint (C) is 18" above the ground (ie: Point D).

Which question is it you want answered?
 
BrunMar said:
In need to know the rise of an arc. If that's what you call it.
I have an 8 foot pipe. If point A is one end and point B the other, with point C being the center of the pipe and D being the ground. How far will point C rise from point D if point B is pushed 2 feet closer to point A. Wouldn't point C simply rise 2 feet? No, because if I would push A all the way to B (8ft), that would bend the pipe perfectly in half putting C only 4 feet from D.
Ok, so then, I have a 6 foot span i wish this pipe to arch over. How long would the pipe need to be if I wanted point C to be 18in from point D, with A & B obviously being on opposite ends of the span.
Click to expand...
Is this homework or a "real life" question?
 
BrunMar said:
In need to know the rise of an arc. If that's what you call it.
I have an 8 foot pipe. If point A is one end and point B the other, with point C being the center of the pipe and D being the ground. How far will point C rise from point D if point B is pushed 2 feet closer to point A. Wouldn't point C simply rise 2 feet? No, because if I would push A all the way to B (8ft), that would bend the pipe perfectly in half putting C only 4 feet from D.
Ok, so then, I have a 6 foot span i wish this pipe to arch over. How long would the pipe need to be if I wanted point C to be 18in from point D, with A & B obviously being on opposite ends of the span.
Click to expand...
Does this diagram correctly show the situation? The pipe is shown in blue and makes a circular arc going through the points ACB.
pic.png

If the above is correct then I would proceed by finding point E (the midpoint of line AC), then point F (the centre of a circle that goes through ACB), and then an equation could be written that locks together these three quantities...
- the length of pipe ACB
- the length AD
- the length CD

The question from blamocur is important.
 
I suspect this may be more what s/he's after... 🤔
(Wants to know the length of the blue line from A to B.)

pic.png
(Courtesy of @Cubist. 😉)​
 
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