What happens exactly, depends on what happens downstream of pipes A and B.
Suppose both pipes flow into the open air, then the pressure at both outlets has to be the same, e.g, at ambient pressure $p_0$ (ignore altitude etc effects). The pressure at the branch is some pressure $p_1$, which is the same for both pipes. In other words
$$\Delta p_A = \Delta p_B $$.
This pressure drop, follows from, e.g. the Hagen-Poiseuille equation,
$$\Delta p \propto L Q, $$
with $L$ the length of the pipe, and $Q$ the flow rate. The scaling can be exactly derived for laminar flow, but for turbulent flow (which you probably have), it relation is similar, with a different proportionality. In other words, the lengths and flowrates in both pipes, are relates as follows.
$$\frac{L_A}{L_B}=\frac{Q_B}{Q_A}$$
Example: If pipe A is three times longer than pipe B, than three times more liquid will flow through pipe B. Thus $75 m^3/h$ through B, and only $25 m^3/h$ through pipe A.
I answer my own question and give a good thanks to DavidPh, who has not really gave the answer, but in fact, it was impossible for him to give it. Here is "why":
I'm French, so I've many fire hydrant data but from France. And when applying them to the formulas, the result was wrong...
In fact, the problem is not the formula but the way we measure the pressure and from vocabulary confusion.
In France, firefighter consider that a fire hydrant must provide a flow rate of 60m3 per hour, so 1000 liters per minute, at a pressure of 1 bar.
In order to check that, here is how we do:
- Put a manometer and a valve at hydrant output
- Open water
- Close slowly the valve in order to increase pressure
- When pressure is at 1 bar, measure flow rate which must be higher than 1000 liters per minute
This mean we change the diameter, in order to get 1 bar. So the formular cant' applied as i fact, we don't know the diameter we have.
This explain also why , in the USA, some fire hydrants flow 7000 liters per minutes when in France they flow only 2000. But in the USA, they flow at a low dynamic pressure when in France the flow is measured at 1 bar dynamic pressure.
Best regards to you all
Peter
Best Answer
If the flow is laminar, i.e. not turbulent, then the relationship between flow rate and pressure is given by the Hagen–Poiseuille equation:
$$\text{Flow rate} = \frac{\pi r^4 (P - P_0)}{8 \eta l}$$
where $r$ is the radius of the pipe or tube, $P_0$ is the fluid pressure at one end of the pipe, $P$ is the fluid pressure at the other end of the pipe, $\eta$ is the fluid's viscosity, and $l$ is the length of the pipe or tube.
For turbulent flow there is no simple analytic treatment, but there is an empirical equation called the Darcy–Weisbach equation:
$$ P - P_0 = f_D \frac{l}{2r} \frac{\rho V^2}{2} $$
where $V$ is the flow velocity and $f_D$ is an empirically measured constant called the Darcy friction factor.
There is an online calculator for the Darcy-Weisback equation here.