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Streamlines and Fluid Flow

(Please refer to the attachment)

Streamlines represent the path of the flow of a fluid. You can imagine that they represent a time-exposure photograph that shows the paths of small particles carried by the flowing fluid. The figure (see attachment) shows streamlines for the flow of an incompressible fluid in a tapered pipe of circular cross section. The speed of the fluid as it enters the pipe on the left is v1. Assume that the cross-sectional areas of the pipe are A1 at its entrance on the left and A2 at its exit on the right.

a). Find F1, the volume of fluid flowing into the pipe per unit of time. This quantity is also known as the volumetric flow rate.
Express the volumetric flow rate in terms of any of the quantities given in the problem introduction.

b). Because the fluid is assumed to be incompressible and mass is conserved, at a particular moment in time, the amount of fluid that flows into the pipe must equal the amount of fluid that flows out. This fact is embodied in the continuity equation. Using the continuity equation, find the velocity v2 of the fluid flowing out of the right end of the pipe. Express your answer in terms of any of the quantities given in the problem introduction..

c). If you are shown a picture of streamlines in a flowing fluid, you can conclude that the __________ of the fluid is greater where the streamlines are closer together.

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Solution Preview

a) In one sec the molecules of the fluid just entering the left end of the pipe will have travelled a distance v1. Therefore, Volume of the fluid ...

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