Starting and stopping flows

The previous examples have been for steady flows. The momentum balance is powerful enough to deal with unsteady flows as well. Two very simple examples illustrate this power. 

Here the steady-state behavior can be found by Bernoulli s equation from point 1 to point 3 

To estimate the starting behavior, we take as our system the pipe from its entrance, point 2, to its exit, point 3. Here we can assume that the pressure at 

Long pipe with quick opening and closing valve. 

Here the shear force acts in the direction opposite to the pressure force at steady state they jwill be equal. Replacing t by its expression in terms of the friction factor and expressing the mass of the system in terms of its volume and density, we find j 

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