Q.  I have a manifold that is 1” OD tubing with 24 outlets of ¼ inch tubing. A needle valve is installed in each of the ¼ inch branching lines and throttled to regulate a flow of ~3 cc/min. The supply pressure into the manifold is 100 psig. What will happen to the system if I close 12 of the 24 needle valves, the inlet pressure to the manifold will be maintained at 100 psi. Will the flow rate in the remaining 12 open needle valves double?

A.  This is a very interesting question, and the results vary based on the diameter and length of the manifold, along with the number and flow rates through each branch. This system is referred to as a network in which there are multiple pipes with multiple destinations with all the needle valves throttled to a specific value. In a network when you change any parameter every parameter will vary. In other words by closing half of the needle vales will affect the flow rate in the other valves, but as we will see sometimes the change in the flow rate through the remaining branches will not change significantly. 

One thing to notice that the flow rates through each one of the needle valves is very small ~3 cc/min. With that flow rate through a ¼ inch tube the losses would be extremely low. In addition, with a flow rate of 72 cc/min or .2 gpm through a 1 inch tube there is minimal head loss in the manifold as well. As a result you can assume the inlet pressure to each of the branch lines will be identical to the regular outlet pressure of 100 psi. Since each needed valve is adjusted for 3 cc/min isolating half of the needle valves will not affect the flow rate through the remaining valves.