Flow rate distribution on multiple branch

[Antares]

Let say I have a simple fan/duct system delivering air at standard conditions with one branch at inlet and one branch at discharge. The fan is operating in its stable region with known flow rate and system pressure.

Now if I add a branch on the inlet side (not necessarily at the fan) to create a slit and assuming that the fan is still operating at the same speed.

With this addition, the system flow rate will increase if system pressure is decrease and vice versa (because the fan is operating at the same speed). The flow rate on the less restricted branch will be higher than the flow rate on the more restricted branch (pressure drop).

What I'd like to know if it is possible to precisely calculate the flow rates in those branches or how the flow rates redistribute in the split?

 

[Evalesco]

You can calculate the flow rates in those branches by using the Bernoulli equation. The Bernoulli equation will help you calculate the pressure, velocity, and density of the fluid at different points in the system. Knowing the pressure drop across the split will help you determine the flow rate in both branches. You can also use a computer simulation to predict the flow rate in both branches.