Question $2(25$ Marks $)$

A horizontal tube has different cross sections at point A and B$.$ The areas of cross section are $A_1$ and $A_2,$ respectively, and pressures at these points are $p_1=g{h}_1$ and $p_2=gg{h}_2,$ where $$ is the density of liquid flowing in the tube and $h_1$ and $h_2$ are heights of liquid column in vertical tubes connected at A and $B.$ If $h_2-h_1=h,$ determine the flow rate of the liquid in the horizontal tube. See figure Q $2.$

Figure Q$2$