Flow Rates through multiple Valves

[CrazyDiamond]

Lets say I have a pump with infinite input. The pump is connected to a valve (V) that has a maximum flow rate capacity of 10 units per second (i.e. 0 to 10 units). This Valve is now connected to two valves in parallel (VA and VB), each identical to the first valve(i.e. max flow rate of 10 units per second each).

Now, my question is - If I set V to 10 units/sec and VA to 8 and VB to 7, what will be the flow rates through each of the valves ? Will the relation be linear (In that case, VA flow: 5.33 and VB flow: 4.67) or is there some other formula ?

On another (not unrelated) note - has anyone here worked with the DURESS-2 system ? Shot in the dark...

 

[stewartcs]

Lets say I have a pump with infinite input. The pump is connected to a valve (V) that has a maximum flow rate capacity of 10 units per second (i.e. 0 to 10 units). This Valve is now connected to two valves in parallel (VA and VB), each identical to the first valve(i.e. max flow rate of 10 units per second each).

Now, my question is - If I set V to 10 units/sec and VA to 8 and VB to 7, what will be the flow rates through each of the valves ? Will the relation be linear (In that case, VA flow: 5.33 and VB flow: 4.67) or is there some other formula ?

The total flow rate at the outlets must equal the total flow rate at the inlets (conservation of mass). If you flow 10 gpm from valve V, then the valves VA and VB will flow a portion of the 10 gpm (a combined total of 10 gpm) based on their flow coefficients.

For example, if the inlet is flowing 10 gpm, and valve VA is flowing 6 gpm, then valve VB must be flowing 4 gpm.

A simple example using the continuity equation will show that the flow rate through each segment is a function of the ratio of the cross-sectional areas of the pipes.

CS

 

[stewartcs]

Here are some examples: http://www.engineersedge.com/fluid_flow/continuity_equation.htm

CS

 

[FredGarvin]

Think about resistors in parallel. The valve with the least resistance to flow will get the larger flow, i.e. flow coefficient, inlet piping, exit piping etc...