Two narrow tube of diameters $d_1$ and $d_2$ are joined together to form a Utube open at both ends. If U-tube contains water, the difference in water levels in the limbs is ( $T$ is the surface tension of water, angle of contact is zero and density of water is $\rho, g$ is the acceleration due to…

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Two narrow tube of diameters $d_1$ and $d_2$ are joined together to form a Utube open at both ends. If U-tube contains water, the difference in water levels in the limbs is ( $T$ is the surface tension of water, angle of contact is zero and density of water is $\rho, g$ is the acceleration due to gravity)

Aicharya · Accepted Answer

Consider the situation below: When angle of contact is zero degree, the radius of meniscus equals the radius of tube. Excess pressure in the first tube $P_1=\frac{4 T}{d_1}$ Excess pressure in the second tube, $P_2=\frac{4 T}{d_2}$ Hence, the pressure difference in the two limbs of the tube is given by, $\Delta P=P_1-P_2=h \rho g$ $\Rightarrow h=\frac{P_1-P_2}{\rho g}=\frac{4 T}{\rho g}\left(\frac{1}{d_1}-\frac{1}{d_2}\right)=\frac{4 T}{\rho g}\left[\frac{d_2-d_1}{d_1 d_2}\right]$

Two narrow tube of diameters $d_1$ and $d_2$ are joined together to form a Utube open at both ends. If…

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