There is a circular tube in a vertical plane

Asked by admin @ 12/08/2021 in Physics viewed by 315 People

There is a circular tube in a vertical plane. Two liquids which do not mix and of densities d1 and d2 are filled in a tube each liquid substends 90° angle at centre radius joining their interface makes an angle alpha with vertical ratio of d1/d2 is

Answered by admin @ 12/08/2021

Let two liquid A and B is filled in a circular tube. density of liquid A is $d_1$ and density of liquid $d_2$ each liquid subtends 90° angle at centre radius joining their interface make an angle $\alpha$ with vertical as shown in figure.

in circular tube, pressure at interface must be the same from both side in equilibrium.

pressure due to liquid A = pressure due to B

or, $P_0+d_1gh_1$ = $P_0+d_2gh_1$

or, $d_1h_1=d_2h_2$

$or,d_1R(cos\alpha-sin\alpha)=d_2R(cos\alpha+sin\alpha)$

or, $\frac{d_1}{d_2}=\frac{cos\alpha+sin\alpha}{cos\alpha-sin\alpha}$

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