Equation of Continuity

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Problems from IIT JEE

Problem from IIT JEE 2008

Statement 1: The stream of water flowing at high speed from a garden hose pipe tends to spread like a fountain when held vertically up, but tends to narrow down when held vertically down.

Statement 2: In any steady flow of an incompressible fluid, the volume flow rate of the fluid remains constant.

  1. Statement 1 is true, statement 2 is true; statement 2 is a correct ex- planation for statement 1.
  2. Statement 1 is true, statement 2 is true; statement 2 is not a correct explanation for statement 1.
  3. Statement 1 is true, statement 2 is false.
  4. Statement 1 is false, statement 2 is true.

Solution: The statement 2 is same as the continuity equation, $Av=\text{constant}$, where $A$ is the cross-section area and $v$ is the fluid velocity. When pipe is held vertically up, the energy conservation makes $v$ to decrease as water goes up and hence $A$ increases by continuity equation. It is the other way around when the pipe is held vertically down.

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References

  1. IIT JEE Physics by Jitender Singh and Shraddhesh Chaturvedi