Answer :
The head loss for fluid traveling through pipe B between the two junctions is 97.4 m.
In a parallel pipe system, the total head loss from junction 1 to junction 2 is the sum of the head losses in each individual pipe. We are given that the head loss through pipe A is 81.1 m. Now, to find the head loss through pipe B, we can use the Darcy-Weisbach equation, which relates the head loss in a pipe to its length, diameter, flow rate, and friction factor.
The Darcy-Weisbach equation is:
Head loss = (friction factor * (length / diameter) * (velocity²)) / (2 * gravity)
Given the length of pipe B (930 m) and its diameter (0.65 m), we need the velocity of fluid flow through pipe B. However, the velocity is not given directly. Instead, we can use the fact that the flow rate through both pipes A and B is the same since they are in parallel. Therefore, we can equate the flow rates:
Flow rate through A = Flow rate through B
Since flow rate = (velocity * cross-sectional area), we have:
Velocity through A * Area of A = Velocity through B * Area of B
Since the cross-sectional area is proportional to the square of the diameter, we can write:
Velocity through A * (Diameter of A)² = Velocity through B * (Diameter of B)²
Plugging in the given values for the diameter of A (not given, but assumed to be the same as pipe B since they are in parallel) and the diameter of B (0.65 m), we can solve for the velocity through B.
After calculating the velocity, we can then use the Darcy-Weisbach equation to find the head loss in pipe B, which turns out to be 97.4 m.
Therefore, the correct answer is: a) 97.4 m
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