Tell me more: the same argument with a few equations
Physics Narrative for 11-14
The argument repeated, with algebra
We can follow the argument about shifting fluid with the help of a few simple equations:
volume of liquid pushed out of the left hand side = cross-sectional area of left hand side × height dropped
volume of liquid pushed into the right hand side = cross-sectional area of right hand side × height risen
But the volumes must be equal, therefore:
cross-sectional area of left hand side × height dropped = cross-sectional area of right hand side × height risen
Rewrite this as:
arealeft × heightleft = arearight × heightright
You can rearrange this to give:
arealeftarearight = heightrightheightleft
So the changes in the heights are just proportional to the cross-sectional areas.