Hi,
i confess that i wanted to help you whithout engaging with the problem,
but i still think you can take it easy,i have written my idea on a paper i would be happy to send it,just email me(khajehzadeh.sina@gmail.com)
Hi,
i think if you're going to take it easy,easily can divide your valve to tree domains,1.the domain between entrance of valve and entrance of the gate(as an example for a gate valve),2.between entrance of gate and gate exit,3.gate exit and valve exit.
then taking use of continuity and energy...