A large tank of (height $h_1=4m$ ) water has a hose connected to it, as shown in figure. The tank is sealed at the top and has compressed air between the water surface and the top. When the water height  $h_2$ is 3 m, the gauge pressure of air $P_1={10}^5{\text{\hspace{0.17em}\hspace{0.17em}N/m}}^2$. Assume that the air above the water surface expands isothermally. The velocity of flow, out of the hose when  $h_2$ has decreased to $2 m$ is  $\sqrt{xg}$. Assume ideal fluid flow and  $P_{atm}={10}^5{\text{\hspace{0.17em}\hspace{0.17em}N/m}}^2$. The value of $x$ is (Neglect viscosity of liquid)