sbmethod3 - The Shell Momentum Balance: Step-by-Step Method...

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The Shell Momentum Balance: Step-by-Step Method CBE 320, DJK, Fall 2009 Step 1: Draw a (crude) picture and list assumptions What velocity components are nonzero? What spatial variables does the velocity depend on? Choose coordinate system. Start a list of assumptions. Step 2: Select system Draw a second picture, showing the “shell” in detail. “Shell”: a ‘box’ with sides b or to the velocity v . box faces should lie on coordinate surfaces (you choose your coordinate system to guarantee this). Make shell thin in the direction the velocity is varying. You will develop intuition about how to do this as you work prob- lems. Step 3: Apply conservation of momentum (compo- nent of interest) Rate at which momentum is transported into the system { { Rate at which momentum is transported out of the system { Force of gravity acting on the system { + = 0 - f d t r ij ij ij i j = + + p v v add other body forces here (e.g., electrical, magnetic,
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