A large, sealed cylindrical tank is filled with an ideal, incompressible fluid of density \(\rho\) to a total height \(H\). The air in the space above the fluid is maintained at a constant gauge pressure of \(P_G = 4\rho g H\). A small hole is opened in the side of the tank at a depth \(d = 0.5H\) below the fluid's surface, and the fluid exits with speed \(v_1\). If the top of the tank were instead open to the atmosphere and the hole remained at the same depth, the fluid would exit with speed \(v_2\).

What is the ratio \(v_1 / v_2\)?