If I understand your problem correctly, you'll need a little more information to find out what you need.
Do you have the available pressure or fluid velocity?
Dynamic pressure in fluid flow is
P = ρ . v^2 / 2
Where:
P = Dynamic pressure (Pa)
v = Velocity (m/s)
ρ = Fluid Density (kg/m3)
Using this formula we can solve for velocity.
v = (2*P/ρ)^0.5
Now we can apply the flow rate formula:
Q = v.A
Where:
Q = Volumetric Flow Rate (m3/sec)
v = velocity (m/s)
A = Area (m2)
This will give volumetric flow rate at given pressure. It won't matter what area you use (inlet, outlet, or in between) as flow rate is constant under constant pressure (how I'm imagining this problem). Velocity will change with cross sectional area but it doesn't sound like you're particularly interested in velocity.
The length won't affect flow rate if you ignore friction. Even taking friction into account will only reduce the flow rate by a significant amount on a very low manifold (how long are we talking?).
Also keep in mind the first equation is for laminar flow (I think.. it's late here and brain's switched off for the night). Google 'laminar flow' if you're unfamiliar with the concept. I'd guess you'd be passing either water (or similar viscosity) or air through this manifold and I'd expect it to be in the turbulent region, not laminar flow. I dont' know how to accurately calculate this information for non-laminar flow.
Hope this helps.