As the stream of water leaves the faucet with cross section At, it is traveling

Question

As the stream of water leaves the faucet with cross section At, it is traveling at velocity v1 As the water continues to fall, it undergoes acceleration due to gravity and Select as it falls. Thus the bottom part of the water stream is falling the top part. In a section of flowing water with the larger cross section area,A_1 the velocity V_1 is and in a section of flowing water with the smaller cross section,A_2 the velocity V_2 the velocity V_2 is Select. Since water is an incompressible fluid and follows the laws of conservation of mass, we can surmise that A_1V_1 A_2 V_2In the case of the falling water, since v_1 v_2, it must be true that A_1 A_2, Which means the water stream narrows as it falls.

Explanation / Answer

As it falls due to acceleration, it increases its velocity as it falls.

Hence bottom part is falling faster than the top part

Larger cross section area A1, velocity v1 is lower

Smaller cross section area A2, velocity v2 is higher

Due to law of conservation of mass and incompressibility of the fluid d*A1v1 = d*A2v2 => A1v1 = A2v2

v1 < v2 [since velocity of water increases as it falls]

A1 > A2 [since, A1v1 = A2v2 and v1 < v2]

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