A rigid, cylindrical diving bell of height \(H\) and cross-sectional area \(A\) is open at the bottom and closed at the top. The bell initially contains air at atmospheric pressure \(P_0\) and temperature \(T_0\). It is slowly lowered vertically into water of density \(\rho\) until its top surface is at a depth \(d\) below the water surface, while the trapped air remains at constant temperature \(T_0\). Water enters through the open bottom and rises to a height \(h\) inside the bell. Which of the following equations correctly relates the height \(h\) to the given parameters?