$A$ glass capillary tube is in the shape of a truncated cone with an apex angle $\alpha$ so that its two ends have cross sections of different radii. When dipped in water vertically,water rises in it to a height $h$,where the radius of its cross section is $b$. If the surface tension of water is $S$,its density is $\rho$,and its contact angle with glass is $\theta$,the value of $h$ will be ($g$ is the acceleration due to gravity).

$A$ long capillary tube of mass $\pi \,g$,radius $2\,mm$ and negligible thickness,is partially immersed in a liquid of surface tension $0.1\,N/m$. Take the angle of contact as zero and neglect the buoyant force of the liquid. Find the force required to hold the tube vertically. $(g = 10\,m/s^2)$

According to Poiseuille's law,the pressure drop per unit length required to overcome viscous forces is $\Delta P = \frac{8 \eta v}{r^2}$,where $r$ is the radius of the cross-section,$v$ is the fluid velocity,and $\eta$ is the coefficient of viscosity. $A$ capillary tube of radius $a$ is dipped in a liquid of density $\rho$,surface tension $T$,and coefficient of viscosity $\eta$. The liquid starts rising in it so that its height $h(t)$ is a function of time $t$. The resulting rate of change of the momentum of the liquid column in the capillary (taking vertically up to be the positive direction and the contact angle to be close to $0^{\circ}$) is $-\pi a^2 \rho gh + F$. Then $F$ is ($g$ is the acceleration due to gravity):

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Three liquids of densities $\rho_1, \rho_2$ and $\rho_3$ (with $\rho_1 > \rho_2 > \rho_3$),having the same value of surface tension $T$,rise to the same height in three identical capillaries. The angles of contact $\theta_1, \theta_2$ and $\theta_3$ obey:

One end of a capillary tube is dipped in water,the rise of water column is $h$. The upward force of $98 \text{ dyne}$ due to surface tension is balanced by the force due to the weight of the water column. The inner circumference of the capillary is (surface tension of water $= 7 \times 10^{-2} \text{ Nm}^{-1}$) (in $\text{ cm}$)