A `U-`tube is made up of capillaries of bores `1 mm` and `2 mm` respectively. The tube is held vertically and partically filled with a liquid of surface tension `49 "dyne"//"cm"` and zero contact angle. Calculate the density of the liquid of the difference in the levels of the meniscus is `1.25 cm`.

Answer

`0.7991 g//cm^(3)`

Explanation

From the moment the filling begins to the moment of time `A` (figure) the water level will uniformly rise in the capillary tube (curve) and remain at the same level int eh broad tube (curve `II`).

The difference in the levels will constatly increase (figure). At the moment of time `A` the difference in the level will reach `h_(0) = (2alpha)/(gr)`
From this moment up to the moment of time `B` the levels in the capillary and broad tube will rise with the same velocities while the difference in the levels will remain constant and equal to `h_(c)`.
At the moment of time `B` are the water level in the capillary tube will reach the end of the capillary and will stop at a height `h_(1)` (figure). From the moment `B` to the moment `D` the water level will continuosly rise in the broad tube. The water level in the capillary will remain constant but the meniscus will change its shape from concave of radius `r` (at the moment `B`) to a float one (at the moment `C`) and then to a convex one of radius `r` (at the moment `D`). The difference in the levels in the section -` BC` will decrease to zero and in the section `CD` it will change its sign and will increase to `h_(2)`.
At the moment `D` the water will begin to flow out of the capillary tube and from this moment onwards all the levels will be constant. The maximum height to which the water rises in the broad tube is `h_(1) + h_(2)`. The maximum difference in the levels is `h_(2)`.
At the moment `D` the water will begain to flow out of the capillary tube and from this moment onwards all the levels will be constant. The maximum height to which the water rises in the broad tube is `h_(1) + h_(2)`. The maximum difference in the levels is `h_(0)`...