Answer:
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.
