Water flows with velocity v$2$v$2$ from a container $($which is open to atmosphere, has a column of water in it of height z$1$z$1$ and with cross sectional area A$1$A$1)$ through a small opening $($of area A$2$A$2)$ at the bottom. Using mass conservation, write an expression for the rate of change of the height of water v$1$v$1$ in terms of A$1,$A$2$A$1,$A$2$ and v$2$v$2.$ Note: this is a STACK question which requires an expression as an answer and all subscripts must be written with an underscore. Please do not rely on the STACK interpreter for accurate display of subscripts.