Figure P12.49 shows a piping system with frictional losses of (h_{mathrm{L} 1-2}=4.0 Q^{2}), with (h_{mathrm{L} 1-2}) in

Question:

Figure P12.49 shows a piping system with frictional losses of $h_{\mathrm{L} 1-2}=4.0 Q^{2}$, with $h_{\mathrm{L} 1-2}$ in $\mathrm{ft}$ and $Q$ in $\mathrm{gal} / \mathrm{min}$. The turbine performance characteristics are given by $h_{t}=20+12.0 Q$, where $h_{t}$ is the turbine head in $\mathrm{ft}$ and $Q$ is in $\mathrm{gal} / \mathrm{min}$. Find the flow rate $Q$.

Figure P12.49