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A capillary tube of radius r and height h1 is connected to a large tube as shown in Fig. The large tube is gradually filled by drops of water falling at equal intervals of time. Draw a graph showing how the level of water in each tube and the difference in levels change with time. Calculate the maximum height of the water in the large tube and the greatest difference in the levels. The surface tension of water is α.

 

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From the moment the filling of the tube commences to the time A (Fig.) the level of the water rises uniformly in the capillary tube (curve I), but remains stationary in the wide

tube (curve II). The difference in the levels will continuously increase (Fig.). At time A the difference in the levels attains the value

From this time to the time B the levels in the capillary tube and in the wide tube rise at the same rate, and the difference in levels will remain at a constant value h0.

At the time B the level of the water in the capillary tube reaches the top of the capillary and remains at the height h1(Fig.). 

From the time B to the time D the level of the water in the wide tube rises continuously. In the capillary tube, the level of the water remains unchanged, but the shape of the meniscus changes from concave with radius r (at time B) to convex with radius r (at time D). The difference in the levels on segment BC decreases to zero; on segment CD it changes sign and increases to the value h0 .

At the time D the water begins to spill over from the capillary tube, from then on the levels are constant.

The greatest height of the water in the wide tube will be h1 +h0. The greatest difference in levels will be h0.

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