Chapter 10, Problem 23Q

To determine

To Explain: The steam of the water from a faucet becomes narrower as it falls.

Explanation of Solution

Introduction:

As the waterfalls, the speed of the steam is increased. So, its cross section must be narrower to balance the flow rate. So, the cross section of the stream becomes thinner. As a result of it, the stream of the water becomes narrower during the falling down.

According to the dependency on the density of the fluid is given as,

  ${\rho }_1\times A_1\times v_1={\rho }_2\times A_2\times v_2$

Where, ${\rho }_1\text{and}{\rho }_2$ are the densities at the two cross section, $A_{1}and{A}_2$ are the respective areas and $v_1\text{and}{v}_2$ are their respective velocities.

The velocity of water is constants, therefore, ${\rho }_1={\rho }_2$

Then the above relation becomes,

  $A_1\times v_1=A_2\times v_2$

According to this equation, at the lower points in the stream, the cross-section is smaller and the velocity at the lower point in the stream must be higher. Therefore, when the stream of water falls then it also gets accelerates. Since the water’s density is constant and then the water tends to hold together. As the result of it the stream of the water becomes narrower.

Conclusion:

As a result of it, the speed of the water stream is increasing during the falling process and hence, its cross section is becomes narrower.