Pressure
Properties of Matter

Tell me more: the same argument with a few equations

Physics Narrative for 11-14 Supporting Physics Teaching

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.

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