As shown in figure lower portion of the manometer tube contains fluid of density `rho_(1)` and the upper part contains fluid of density `rho_(2)(rho_(1)gtrho_(2))` .
If pressures on the top of these two arms are `P_(1)andP_(2)`, calculate pressure differnce `(P_(1)-P_(2))`.

Explanation

Consider points A and B , as shown in the diagram , at equal height from bottom. For these points ,
`P_(A)=P_(B)`
`thereforeP_(1)+(h+x)rho_(2)g=xrho_(2)g+hrho_(1)g+P_(2)`
`thereforeP_(1)-P_(2)=xrho_(2)g+hrho_(1)g-hrho_(2)g-xrho_(2)g`
`thereforeP_(1)-P_(2)=(rho_()-rho_(2))hg`