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The thirteen equations derived above contain algebraic expressions for flows, level, differential pressure, fractional valve openings and demanded valve travel, as well as expressions for the rate of change of liquid mass and for the rate of change of valve travel for each valve. Given a knowledge of the constants contained in our equations, we can calculate all these algebraic expressions at any instant in time, once we know the present values o f the liquid mass in the tank and o f the three valve travels. These last four variables are vital indicators of the condition of the system, and are called the 'state variables' or, more colloquially, the 'states' of the system. What prevents the flow of the calculation being circular is that we may integrate numerically the state derivatives with respect to time from any given starting values for the state variables to find their values at any later time. At time to, the liquid mass and the valve travels will be at their initial conditions, assumed known:

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