A bypass piping network is shown in the figure below. The velocities and the Fanning friction factors

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A bypass piping network is shown in the figure below. The velocities and the Fanning friction factors will be approximately equal in the straight pipe as well as in the bypass loop, while either one of them is in operation. Determine the required ratio of the diameter of the straight pipe to the diameter of the bypass loop to maintain identical pressure loss in the two systems, while each is in operation. 

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