As a fluid flows into a constriction in a pipe, the a. increases b. stays the same c. decreases d. is independent of the area change of the constriction

The velocity in the pipe constriction will increase. (option A)

Explanation:

Assuming the flow to be subsonic, that is, a flow speed less than the speed of the sound (around 323 m/s for standard condition of 15 °C), in a constriction, the pipe sectional area is reduced then, to satisfy the fluid continuity equation, the  flow's speed must increase.

The continuity equation states that the amount of fluid must be conserved:

m=p.A.V=k=constant

Where m is the mass rate, p the density, A the sectional area and V the fluid's speed. If we consider incompressible flow (p constant):

m=A.V=k=constant

Therefore by applying the continuity equation before and at the constriction:

A.V=Ac.Vc

(the subscript c related to the constriction)

Solving for Vc:

Vc=V.(A/Ac)

As A/Ac must be bigger than 1 because of the constriction therefore

Vc=V.(Ac/A>1)>V.

The velocity in the constriction is greater than before the constriction.

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