Writing the initial water height as zin

$($i$.$e$.$ at t$=0$

z$1=$zin

$),$ give an expression for the height of the water in the cylinder as a function of time. If you have made any assumptions based on the geometry, these need to be included in the answer. $($Note: this is a STACK question which requires an equation 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. zin

is written as z$\_$in$)$