# Simple fluids but is the application correct

## Homework Statement

problem states that .... there is a u tube and filled with liquid of densities ρ and 2ρ. the base lenght of the tube is 'l'. now it is accelerated towards right with accl.=a. if the HEIGHT DIFFERENCE AFTER ACCELERATING THE SYSTEM IS '0'. then what was the height difference before acceleration??

## Homework Equations

P=ρgh; F=ma ; F=(ρ.V)a ;

## The Attempt at a Solution

i tried to find pressure at bottom most level at interface of the two liquids, then the net force, then applied newtons 2nd law, but could'nt get the solution...

## The Attempt at a Solution

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tiny-tim
Homework Helper
hi phyeinstein_c!

hint: what will be the angle of the surface of the fluid (in either half of the 'U') ?

lets see...if the u tube is moving towards right the major driving force is on the left side of the tube. since the heights are equal the 2p liquid is in the left tube .

first find relations between height h1 and h2 in the two sides of tube when at rest...then find height h when accelerated.. then keeping volume constant use h1 + h2 = 2h

hi phyeinstein_c!

hint: what will be the angle of the surface of the fluid (in either half of the 'U') ?
they're not at angle. initially they are at a height difference. thats it is wat is given.

tiny-tim
Homework Helper
i know, i mean, suppose there was only one pipe (or a jar or vase), what would be the angle of the water surface?

it wud be horizontal obviously

tiny-tim
Homework Helper
nope!

why...???

tiny-tim
Homework Helper
suppose the water was ice, and the surface was at an angle, and a drop of water was on the surface …

what angle would the surface have to be for the drop of water to stay where it is?

<=45 i guess

tiny-tim
Homework Helper
<=45 i guess
how do you get that?

:P just guessing... mgsinθ is equal to the friction acting.. of surface tension watever... unless u describe the surface of ice to be smooth....

tiny-tim
Homework Helper
… unless u describe the surface of ice to be smooth....
yes, of course it's smooth!

ok... then it cant stay where it is..

tiny-tim