Question

A glass capillary sealed at the upper end is of length 0.11 m and internal diameter . The tube is immersed vertically into a liquid of surface tension . To what length has the capillary to be immersed so that the liquid level inside and outside the capillary becomes the same? What will happen to the water level inside the capillary if the seal is now broken?

Solution

Correct option is

 

If A is the cross-sectional area of the tube and L its length, the initial volume of air inside it will be V1 = AL while pressure p1 = p0 = atmospheric pressure.

Now when the tube is immersed in water wit

h its length x in water, the level of water inside and outside is same; so the volume of air in the tube will beV2 = A(L – x). Further if p2 is the pressure of gas in the tube, 

          

Now if temperature is constant, 

          

             

  

  

If the seal is broken the pressure inside the capillary will become atmospheric, i.e., p0 while capillary will take place and the rise will be    

          

However, the length of the tube outside the water is 0.11 – 0.01 = 0.1 m; so the tube will be of insufficient length and so the liquid will rise to the top of the tube and will stay there with radius of meniscus, 

          

             

                  

SIMILAR QUESTIONS

Q1

Water flows through a capillary tube of radius r and length l at a rate of 40 ml per second, when connected to a pressure difference of h cm of water. Another tube of the same length but radius r/2 is connected in series with this tube and the combination is connected to the same pressure head. Calculate the pressure difference across each tube and the rate of flow of water through the combination.  

Q2

 

Spherical particles of pollen are shaken up in water and allowed to settle. The depth of the water is . What is the diameter of largest particles remaining in suspension on hour later?

   

Q3

A cylindrical vessel of area of cross-section and filled with liquid to a height of h1 has a capillary tube of length 1 and radius r protruding horizontally at its bottom. If the viscosity of liquid is , density  and g = 9.8 m/s2, find the time in which the level of water in vessel falls to h2.

Q4

Vessel whose bottom has round holes with diameter of 1 mm is filled with water. Assuming that surface tension acts only at holes, find the maximum height to which the water can filled in the vessel without leakage. Given that surface tension of water is 

Q5

A ring is cut from a platinum tube of 8.5 cm internal and 8.7 cm external diameter. It is supported horizontally from a pan of a balance so that it comes in contact with the water in a glass vessel. What is the surface tension of water is an extra 3.97 g weight is required to pull it away from water? (g = 980 cm/s2)

                                                                

Q6

A mercury drop of radius 1 cm is sprayed into 106 droplets of equal size. Calculate the energy expended if surface tension of mercury* is .

Q7

The lower end of a capillary tube of diameter 2.00 mm is dipped 8.00 cm below the surface of water in a beaker. What is the pressure required in the tube to blow a bubble at its end in water? Also calculate the excess pressure. [Surface tension of water  density of water = 103kg/m3, 1 atmosphere 

Q8

The limbs of a manometer consist of uniform capillary tubes of radii . Find out the correct pressure difference if the level of the liquid (density 103 kg/m3, surface tension ) in narrower tube stands 0.2 m above that in the broader tube. 

Q9

Two separate air bubbles (radii 0.002 m and 0.004 m) formed of the same liquid (surface tension 0.07 N/m) come together to form a double bubble. Find the radius and the sense of curvature of the internal film surface common to both the bubbles. 

Q10

A conical glass tube of length 0.1 m has diameters 10–3 and  at the ends. When it is just immersed in a liquid at 0oC with larger diameter in contact with it, the liquid rises to  in the tube. If another cylindrical glass capillary tube B is immersed in the same liquid at 0oC, the liquid rises to  height. The rise of liquid in the tube B is only  when the liquid is at 50oC. Find the rate at which the surface tension changes with temperature considering the change to be linear. The density of the liquid is  and angle of contact is zero. Effect of temperature on density of liquid and glass is negligible.