Conservation of momentum in a pipe

We now substitute (3.71) into (3.70), cancel out terms, divide by SxSt, then let if 0 to give  

Assuming once more that the right-hand side of this equation can be subjected to a finite-difference scheme, equation (3.73) provides a further equation in dc/df and dv/dt, so that in equations (3.58) and (3.69) and (3.73) we have three equations in the three unknowns av/at, au/at and ac/at. But we should note that the right-hand side of (3.73) contains not only c and v, but also pressure p. Also, we should note that in practice, we will want to know also the temperature 7 as a function of time and space. Since v and u are independent thermodynamic functions, it is possible to express a third, such as pressure or temperature. 

Rgura 3.B Element of pipe showing the forces acting. 

At this stage, we have three equations in the three unknowns dp/dt, dT/dt and dc/dt, and we use the relations  

BNES (1980). Boiler Dynamics and Control in Nuclear Power Stations 2, Proceedings of the Second International Conference held in Bournemouth, 23-25 October 1979 (British Nuclear Energy Society, 1980), particularly the following papers  

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