Final answer:
The problem requires an engineering design of an optimal pipeline system for transporting milk. A graphical cost analysis and a drawing of the pipeline layout are essential to the solution.
Step-by-step explanation:
To determine the appropriate prevalence of steel pipe to be used in the dairy factory's pipeline, we need to consider the flow rate of the milk and the pressure required for the pump to transfer the milk into the storage tanks. The flow rate can be calculated by applying Bernoulli's equation, which relates the velocity of the fluid to the pressure difference and the density of the fluid. The pressure required for the pump can be determined by considering the height difference between the pump and the storage tanks, as well as the friction losses in the pipeline.
By analyzing the given information about the pipeline, we can calculate the corresponding flow rate and pressure required. Then, we can use these values to determine the appropriate diameter of the steel pipe, taking into account the material properties and the desired flow rate. The economic design of the pipeline can be determined through cost analysis, considering the costs associated with the different pipe diameters and other components of the pipeline.
To provide a complete solution to the problem, we would need the specific values of the flow rate, pump efficiency, height difference, and other relevant parameters. Additionally, a graphical presentation of the cost analysis and a drawing of the pipeline would require more detailed information about the pipeline layout and component specifications.