Constrained pressure at the inlet to a liquid pipeline

Assuming Euler integration, and using a subscript terminology, the mass in the tank at the jth time instant may be calculated from the mass and the flows at the (j — l)th time instant  

The corresponding pressure at the outlet of the tank/inlet to the line will be calculated as  

To find the flow at the pipe inlet at time j, Wq.j, the backward characteristic, equation (19.31) may Im applied with = I. Since the fluid is assumed to be a liquid at constant temperature, we will assign a constant value to specific volume, v. Thus Wo.y, is given in terms of the current pressure, po.j, and past flows by 

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