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The mass flux of a fluid flowing into one of a container is 3.0 kg/s; the mass flux flowing out The other side of the container is 2.0 kg/s. Assuming the container is completely filled with the fluid and that there are no other ways for the fluid to get in or out, one can conclude that (A) the entrance point has a larger cross-section than the exit point. (B) the magnitude of the entrance velocity is larger than the magnitude of the exit velocity. (C) the density of the fluid inside the container must be increasing. (D) the fluid is incompressible.

The mass flux of a fluid flowing into one of a container is 3.0 kg/s; the mass flux flowing out The other side of the container is 2.0 kg/s. Assuming the container is completely filled with the fluid and that there are no other ways for the fluid to get in or out, one can conclude that
(A) the entrance point has a larger cross-section than the exit point.
(B) the magnitude of the entrance velocity is larger than the magnitude of the exit velocity.
(C) the density of the fluid inside the container must be increasing.
(D) the fluid is incompressible.

Grade:10

1 Answers

Jitender Pal
askIITians Faculty 365 Points
8 years ago
The correct option is (C).
From equation of continuity, the cross-sectional area of the container times the velocity of the fluid times the density of the fluid is constant. It is equal to the flow of mass rate of the fluid.
The mass flow rate of the fluid is 3.0 kg/s in one part of the container and 2.0 kg/s on the other part. From the equation of continuity, the value of mass flow rate of the fluid should remain constant for an incompressible fluid. This is due to that fact the density of the fluid remains constant in an incompressible fluid.
The value of mass flow rate of the fluid changes as the density of the fluid is not uniform throughout the container. Thus, the density of the fluid inside the container must be increased to change the value of the mass flow rate of the fluid.
Therefore, the correct option is (C).
When the entrance point has large cross-section area than the exit point, the speed of the fluid at the entrance point should be lower than at the exit point. This is so to make the mass flow rate of the fluid constant.
Option (A) is not correct.
Option (B) is also not correct.
For an incompressible fluid, the equation of continuity should be strictly followed. As the value of the mass flow rate of the fluid is not same at the two sides of the container, the fluid is not incompressible. Option (D) is not correct.

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