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San Diego State University *

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Mechanical Engineering

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Oct 30, 2023

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AE340 Class # 11 Chapter 5: Viscous Flows (Exact Solutions) Looking more closely on the effects of viscosity, and how we use the no-slip BC! Sometimes, the solutions presented in this Chapter are called: Exact Solutions . The first example is the flow between two parallel plates (the Couette flow). Here, naturally, the Re number ‘pops up.’ Also, the connection between the 1D and 2D models is demonstrated. This example can be extended to explore the problem of hydraulic bearings (not included in this class). The main topic in this Chapter is the flow in pipes – which is similar to the flow between the two flat plates, but defined in cylindrical coordinates. Next is a quick summary of the previous class:
Flow due to the upper plate moPon Flow due to pressure gradient Flow due to combined motion of the upper plate and a negative pressure gradient
The Conservation of Mass Equation: ࠵?࠵? ࠵?࠵? = 0
After integration the velocity profile at any x station is: + = Assuming negaPve dp/dx
Note that dp/dx must be negative for the flow into the right direction.
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