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Finding Vertical Distance in Pipe Line System

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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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