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Flow at the inlet and outlets can be assumed One-dimensional for the sake of simplicity. (a) Explain how this assumption simplifies the Reynolds Transport Theorem equation (provide complete, detailed answer) (b) This assumption introduces errors into the calculations, as it assumes flow properties do not vary across the inlet/outlet area. How this error changes with the area (does it increase or decrease)?

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Answer:

a) reduces the need to determine complicated flow properties.

b) The error decreases with the change in the area.

Explanation:

a) The mechanical properties of a fluid can sometimes be complicated. This results in an a need to calculate all the forces acting on the surface of the fluid particle. This then introduces the concept of the resolving the various forces. To reduce the error, we use the control volume. The  Reynolds Transport Theorem states that the rate of change of an extensive property N, for a system is equal to the time rate of change of N in the control volume and the net rate of flux of the property N through the control surface.

b) By making the assumptions, it decreases the likelihood of errors occurring in the equation.

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