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Volume of a Pipeline

The attached document shows a pipeline of 24 inch diameter (approx. 600mm) buried 1 m below the ground. There is a water pipe which prevents the pipe from going horizontally and hence it has to follow one of two pathways ie. either along the dark blue 5 mm diameter curves and exit at the bottom or along the dotted red double 40 mm diameter curve and join the blue line at the bottom and then exit.

The big diagram is a cross-sectional view of the pipeline and view A is a view looking at the front of the pipeline where flow enters. View A is shown below with all the dimensions given.

The task of this posting is to determine the volume for the section below the ground for the two cases mentioned above ie. the green striped case and the red striped case. One can notice that in the case of the red stripe the trench will have to be dug deeper than in the case of the green stripe case. Note that the dimensions of the bends and other dimensions are not given for fun. Also state any assumptions necessary.

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Solution Preview

See the attached jpg file.

All red bends have the same diameter of 40 mm
All blue bends have the same diameter of 5 mm
The drawing explains why the volumes are equal without any calculations, perhaps with a few words of explanations.
Therefore it is enough to calculate the volume for 0 mm bends.

A few words of proof:

Consider areas 1, 2, 3, and 4 between blue and red lines in the attached enhanced drawing.
These areas represent in fact volumes as similar sections can be drawn parallel to this ...

Solution Summary

The volume of a pipeline is calculated.

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