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Finding Vertical Distance in Pipe Line System

For the system in attachment, calculate the vertical distance between the surfaces of the two reservoirs when water at 10 degrees celcius flows from A to B at the rate of 0.03 m^3/s. Both pipes are cast iron and the elbows are standard. The total length of the 3" pipe is 100 meters. For the 6" pipe, it is 300 meters.

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By writing the energy equation between points A and B and assume the distance between A and B is Z

Pressure at A/density + ½ of square of Velocity at A + gZ = Pressure at B/density + ½ of square of Velocity at B + Losses due to friction in straight pipe sections + losses due to fittings.... (0)

To find all the terms in eq. (0)

Pressure at A = Pa = static pressure at free surface above A + density * g * depth of A below free surface
Since no information is given about the depth of point A below the free surface, the pressure at A is assumed to be atmospheric. The same argument applies to point B and pressure at B = Pb = atmospheric pressure.

The velocity at point A (Va)= discharge / cross section area at point A
= (0.03) / (3.14/4 (0.0909)^2) = 4.62 m/s
The velocity at point B (Vb) = discharge / cross section area at point B
= ...

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