how fast does an infinite plug move in an infinite pipe?

Question

gravitational drainage

this was a HW question word for word. you asked for lengh of pipe even though i wrote it is "INFINITE"

Answer 1

Let v1 = speed of the plug relative to a dot
Let v2 = speed of the infinite pipe relative to a dot
Let phi = angle of the pipe relative to some plane
speed of the pipe along the plane is v2 * Cos(phi)
phi = 0 if we select a plane along the axis of the pipe
Therefore the vector describing the speed of the pipe along the plane is v2*Cos(0) = v2
The plug speed relative to the plane is also found to be v1
An infinite pipe will act like a line that is very far away
The plug will act like a dot moving along that line if it is very far away too
Assume that our origin is very far away from the pipe - if the pipe is infinite then space has to be very big and the assumption is correct for all 3-dimensional space.
The speed of the plug relative to the pipe is v1-v2
v2 = 0 since if it was greater than 0 then it would have taken an infinite amount of energy to move it since it would have an infinite mass and no energy would have been left over to make the plug.
Since the ends of the pipe are infinitely far away then the pipe must have come into existence after the plug
The guy who got the pipe wrapped around the plug would never have been able to do it if the plug was moving
Therefore v1 = 0
If v1=0 and v2=0 then v1=v2
So in fact the plug is stopped relative to the pipe.

Answer 2

there isn't enough time or paper to answer that question. it would depend on
1. geographic location
2. elevation
3. angle of the pipe
4. construction material of the pipe
5. construction material of the plug
6. shape of the plug
7. temperature
8. humidity
9. length of the pipe

these are the questions that would need to be answered just off the top of my head-I'm sure with a little time I could come up with several more that would influence the answer to the question you asked.
next time you want to be a smart as* think about your question or ask a question in a field you have some knowledge in.

Answer 3

hard task. look into on google. that may help!