How the flow is distributed when the water flow from one river/drain to multiple rivers/drains?

Assuming that water ( total amount $Q$) flows down from one river/drain, into multiple rivers/drains, under the action of gravity, as shown below:

How the flow ($Q$) will be divided among different outflows ($Q_i$)?

Assume that we know that

1. The drain geometry is predetermined—we know the $x,y,z$ coordinates of the start and end node of the river/drain and we know the cross sectional information and length of the river/drain
2. The velocity is approximated by manning formula, $$V=frac{k}{n}R_h^frac{2}{3} S^frac{1}{2}$$
3. The flow is incompressible flow, so $Q=VA$

where

1. $R_h$ is the hydraulic radius of the river/drain
2. $S$ is the slope
3. $k$ conversion between the SI and English units
4. $n$ the manning coefficient
5. $A$ is the cross section area of the river/drain

For one, I know that the water flow volume must be conserved

$Q=Q_1+Q_2+Q_3+…$

But I don’t know what are the other factors that could help us determine $Q_i$.

Edit: After some research, I think that I need use Bernoulli equation to include headloss in this calculation, but I have no idea how to do it, how to proceed?