Valve at the inlet to a liquid pipeline

But for our stipulated case of Woj 0, in view of the fact that X is always positive, it is clear first that the positive root must be chosen and secondly that 

For negative flow, equations (19.41b) and (19.42) may be combined to give the quadratic in the pipe entry flow at the yth time instant, W o.y  

Since we have stipulated that the flow shall be negative, it is clear that the negative square root must be taken, and that 

Flgur 19.4 Valve located some distance along the pipeline. 

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