In the pipe network shown in the figure, all pipes have the same cross-section and can be assumed to have the same friction factor. The pipes connecting points $W, N$, and $S$ with point $J$ have an equal length $L$. The pipe connecting points $J$ and $E$ has a length $10 L$. The pressures at the ends $N, E$, and $S$ are equal. The flow rate in the pipe connecting $W$ and $J$ is $Q$. Assume that the fluid flow is steady, incompressible, and the pressure losses at the pipe entrance and junction are negligible. Consider the following statements:
$\text{I}$ : The flow rate in pipe connecting $J$ and $E$ is $Q / 21$.
$\text{II}$: The pressure difference between $J$ and $N$ is equal to the pressure difference between $J$ and $E$.
Which one of the following options is CORRECT?
- $\text{I}$ is True and $\text{II}$ is False
- $\text{I}$ is False and $\text{II}$ is True
- Both $\text{I}$ and $\text{II}$ are True
- Both $\text{I}$ and $\text{II}$ are False