Question about level & gradient calculation?

Question

Given point "A" whose elevation is 40.100m (measured from sea level) and point "B" (elevation not known). Sewerage culvert pipes of 300mm diameter are to be installed starting from point "A" to "B" along a distance of 25.500m with a gradient of 1:450. What is the elevation of point "B"? Please elaborate.

Answer 1

Hi matgadang

A couple of issues with the answer given above:

First, the question suggests to me that the point B is actually lower than point A, since the pipes run from A to B. I'm going to assume B is the lower point.

Secondly, the 25.500m pipe distance is likely to be the inclined distance (ie the distance the pipes actually travel) rather than the horizontal distance as assumed above.

ok

Draw a right triangle whose horizontal side is the level separation of the two points, whose short vertical side is the difference in elevation between A and B, and whose hypotenuse joins A (at the top) to B (at the bottom). We can discover the small angle B between the inclined pipes and the horizontal by the gradient: the gradient ratio gives us the tan of the angle:

tanB = 1/450

B = 0.127 degrees

Now we can use this angle to find the elevation difference, x, since x/hypotenuse is equal to the sin of B:

x/25.500 = sin(0.127)

x = 0.057m

This value x is the drop or difference in elevation between A and B, so B = A - 0.057m

B = 40.043m


Hope this helps!
The Chicken

Answer 2

Easy.

The gradient is 1 m of rise for every 450 m horizontally.
Therefore, for 25.500 m of distance, the rise would be 25.5/450, or 0.057 m. The gradient would usually be expressed as a percent in the US, and this would be 0.222%.

Thus the if the 40.100m elevation is at the invert, the upstream invert would be 40.157m.