Balancing Columns of Liquids 
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Balancing Columns of Liquids : It's used to determine the density of liquid by placing it with another immiscible one of known density in U-tube.

when they are settled, the pressures on the horizontal line at the interface ( separating surface ) are equal .

 

Delta P1 = Delta P2  or   r1h1g1 = r2h2g2                     

or r1h1 =  r2h2

or r1/r2 = h2/h1   also h a 1/r

If one of the liquids is water , RD of liquid =

Hwater/Hliquid = rliquid/rwater

 

If the two liquids are miscible , a separating liquid is used such as mercury where the two interfaces are made to be on the same horizontal level.

if c.s. area of one branch = twice that of the second branch .
the depression in the first = half the elevation  in the second branch .