I have a pipeline system composed by two reservoirs and a control valve at the proximity of the downstream reservoir. I used the method of characteristics to calculate the flow rate and the piezometric head value at the valve level by decreasing its opening percentage.(OP)
For the flow rate value (Q), I had to resolve a function of the second degree (ax2 + bx + c = 0) where x=Q .
I got two values which the first is negative and the other is positive. I didn't know what I have to choose??? Knowing that this value should decrease with each decrease of the (OP).
N.B: the flow rate value will allow me to calculate the piezometric Head value.