Figure P5.101 shows a test rig for evaluating the loss coefficient, \(\mathrm{K}\), for a valve. Mechanical energy losses in valves are modeled by the equation:

\[ g h_{L}=\mathrm{K}\left(\frac{V^{2}}{2}\right) \]

where \(g h_{L}\) is the mechanical energy loss and \(V\) is the flow velocity entering the valve. In a particular test, the pressure gage reads \(40 \mathrm{kPa}\), gage, and the \(1.5-\mathrm{m}^{3}\) catch tank fills in \(2 \mathrm{~min} 55 \mathrm{~s}\). Calculate the loss coefficient for a water temperature of \(20{ }^{\circ} \mathrm{C}\).

Figure P5.101

D = 6 cm Pressure gage Valve D = 4 cm 2 Catch tank