As a fluid flows into a constriction in a pipe, the velocity ... 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.