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For the calculation problem, it is known that the price of steel pipes is proportional to the 1.37th power of their diameter. Now, a fluid with a certain volume flow rate needs to be transported over a certain distance. The following comparison is made between two delivery methods: using two pipes with small diameters and one pipe with a large diameter. (1) What are the costs of the equipment required for each method (assuming the flow velocity inside the pipes is the same in both cases)? (2) If the flow is laminar in the large pipe, then what will be the power required to overcome the pipeline resistance when using those two smaller pipes, as a multiple of the power required in the large pipe?
Reply to 1# Yiyuan: The conditions for the second question are insufficient. Is it laminar or turbulent flow inside the tube at this time? Because both are possible.
There are no other conditions; it only states that the coefficient of friction should be determined using Plücker’s formula. As for the conditions for laminar and turbulent flow, they depend on the value of the Reynolds number. Thank you!
This post was last edited by phlpf2009 on 2011-1-14 09:20. Reply to 1#: Yi Yuan, d∝S0.5; d/D=0.50.5, and m/M=2×0.50.5×1.37=1.244. Thus, the cost is 1.244 times that of the original large-diameter pipe.
d∝S 0.5; d/D=0.50.5; m/M=2×0.5×1.37. Thus, the cost is 1.244 times that of the original large-diameter pipe. Thank you for your answer!
Reply to 1# Yiyuan: Assuming that the flow velocities in the small tube and the large tube remain equal: hf∝d-2; hf2/hf1=0.50×0.5×(-2)=2 (Note: one small tube). Therefore, N2/N1=2×2=4 (times)
Assuming that the flow rates in the small tubes and the large tube are still equal: hf∝d-2; hf2/hf1=0.50×0.5×(-2)=2 (Note: one small tube). Therefore, N2/N1=2×2=4 (times). Thank you for your answer :)