Question

Water is slightly coming out from a vertical pipe. As the water descends after coming out, its area of cross section reduces. Explain this on the basis of the equation of continuity.

Answer 1

In the continous of flow rate, the flow of the volume of the liquid remains constant.

That is, Av = constant.

Also the cross-sectional area of the flow after descending some distance A' and velocity V' then from the continuity equation

A'V' = AV  → A' =A(V/V')  

Since the coming out liquid is falling under gravity,

V'>V  →V/V' < 1 Thus A' < A.  

So, as the water descends the area of the cross section reduces.

Answer 2

Hey.

This Question can be easily explained on the basis of the equation of the continuity,

But, what is the equation of continuity.

Equation of the continuity is the mathematical equation which tells us that if any fluid is flowing in an pipe, then its velocity will be inversely proportional to the area of the cross -section of the tube.

Now, If the water is flowing from top to bottom, then there will be effect of gravity, and its acceleration will be constant equal to acceleration due to gravity.

Now, when it will fall, time interval will continuously increase, but acceleration is constant. This means, velocity must increase to maintains the acceleration constant.

Thus, While falling down velocity of the water increases,

By equation of continuity, if velocity increases, then area decreases, therefore, area of the cross-section of the pipe below decreases.

Hope it helps.