Layout of a water supply system to a small community is shown below. Water is supplied in the main line which is then distributed among 10 houses via branch pipes. The total cost of the system comprises of
Cost of piping material
Cost of the pump
Cost of electricity used by the pump
The aim is to suggest D (diameter of the main pipe) which gives the minimum overall cost of the system.
Units are in meters unless specified.
Following assumptions can be used to simplify the analysis:
In reality, the flow in the branch pipe changes after it supplies water to each house. Same is the case for the main pipe after it has supplied flow to 1st branch pipe. However, for the purpose of this project, it can be assumed that the flow in the main or branch pipe remains constant equal to the flow at its starting point
Pipe length between the pump and the water reservoir is negligible
Pump and its motor are 100% efficient
The water tank of each house is placed on the ground and not on the roof. So, there is no vertical distance between the pump and the tank
Use Table 8.2 (Fluid Mechanics by Munson) can be used to suggest different components required to be installed in this layout. Clearly specify installed locations of these components. Take into account the losses due to these additional components. The cost effect of these components can be neglected.
Any other assumption made needs to be stated clearly
The known data is provided in the table below:
The diameter of main pipe (in the range branch pipe < D < 1m) which is the most cost effective. Also calculate the running cost of the arrangement over a period of 10 years.
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