A liquid is kept in a cylindrical vessel which is being rotated about a vertical axis through the centre of the circular base. If the radius of the vessel is r and angular velocity of rotation is ω , then the difference in the heights of the liquid at the centre of the vessel and the edge is:

Question

A  liquid is kept in a cylindrical vessel which is being rotated about a  vertical axis through the centre of the circular base. If the radius of the  vessel is r      and angular velocity  of rotation is ω     , then the difference in the heights of the liquid at the  centre of the vessel and the edge is:

Infinity Learn · Accepted Answer

From Bernoulli’s theorem,$$PA+12dvA2+dghA$$ $$=PB+12dvB2+dghBHere$$, $$hA=hB$$∴  $$PA+12dvA2=PB+12dvB2PA$$−$$PB=12d$$[$$vB2$$−$$vA2$$]Now, $$vA=0$$ , $$vB=r$$ω  and PA−$$PB=hdg$$∴ $$hdg=12dr2$$ω$$2$$  or $$h=r2$$ω$$22g$$

A liquid is kept in a cylindrical vessel which is being rotated about a vertical axis through the centre of the circular base. If the radius of the vessel is $r$ and angular velocity of rotation is $ω$ , then the difference in the heights of the liquid at the centre of the vessel and the edge is:

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