A liquid flows under steady and incompressible flow conditions from station $1$ to station $4$ through pipe sections $\mathrm{P}, \mathrm{Q}, \mathrm{R}$, and $\mathrm{S}$ as shown in figure. Consider, $d, V$, and $h$ represent the diameter, velocity, and head loss, respectively, in each pipe section with subscripts ' $P$ ', ' $Q$ ', ' $R$ ', and ' $S$ '. $\Delta h$ represents the head difference between the inlet (station $1$) and outlet (station $4$). All the pipe sections are placed on the same horizontal plane for which the figure shows the top view.
Which one of the following options is correct for the given flow loop?
- $\Delta h=h_{P}+h_{Q}+h_{R}+h_{S} \quad$ and $\quad V_{P} d_{P}^{2}=V_{Q} d_{Q}^{2}=V_{R} d_{R}^{2}=V_{S} d_{S}^{2}$
- $\Delta h=h_{P}+h_{Q}+h_{R} \quad$ and $\quad V_{P} d_{P}^{2}=V_{Q} d_{Q}^{2}=V_{R} d_{R}^{2}=V_{S} d_{S}^{2}$
- $\Delta h=h_{P}+h_{Q}+h_{R} \quad$ and $\quad V_{P} d_{P}^{2}=V_{Q} d_{Q}^{2}=V_{R} d_{R}^{2}+V_{S} d_{S}^{2}$
- $\Delta h=h_{P}+h_{Q}+h_{R}+h_{S} \quad$ and $\quad V_{P} d_{P}^{2}=V_{Q} d_{Q}^{2}=V_{R} d_{R}^{2}+V_{S} d_{S}^{2}$
