Concepts of Physics

IIT JEE Physics (1978-2018: 41 Years) Topic-wise Complete Solutions

Pressure in Two Connected Bottles

Objective

To clarify the concept of pressure in an interesting manner.

Procedure

Make holes near the bottom of two bottles and connect them with a transparent pipe. Fill colored water in bottle 1 upto the 3/4 level and keep the bottle 2 empty. Close the cap of two bottles. Open the cap of bottle 2. Let atmospheric pressure be \(p_0\). Ask the following questions:

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  1. Pressure of air in bottle 1 is (i) less than \(p_0\) (ii) more than \(p_0\) (iii) equal to \(p_0\)?
  2. Pressure of air in bottle 2 is (i) less than \(p_0\) (ii) more than \(p_0\) (iii) equal to \(p_0\)?
  3. If the cap of the bottle 1 is opened, what kind of water flow do you expect?
    • No water will flow
    • Some water will flow from bottle 1 to bottle 2
    • Water will be equally divided in both bottles

Discussion

The solution is:

  1. Bottle 1 is open. So pressure in it is \(p_0\). At the tube level pressure in bottle is also the same. As you go up in bottle 1 pressure decreases by \(h\rho g\). So pressure of air in bottle 1 is less than \(p_0\).
  2. \(p_0\) as it is open to atmosphere.
  3. Water will be equally divided in the two bottles.