A municipality’s drinking water network is supplied by a plant that is no longer sufficient to meet growing demand. It is planned to build two other plants which will be connected to the network (see image), where the arrows indicate the direction of the flow). It is necessary to predict the flows in each of the pipes of the network when the plants are operating at full capacity. (a) Construct the system of linear equations that describes the situation, knowing that for each knot in the system, the inflows are equal to the outflows. Identify the variables used. (b) Use an appropriate solution method to find the solution set of the system of linear equations without taking into account the context. (c) Taking the context into account, what can be expected as throughput between the knots N1 and N2?
A municipality’s drinking water network is supplied by a plant that is no longer sufficient to meet growing demand. It is planned to build two other plants which will be connected to the network (see image), where the arrows indicate the direction of the flow). It is necessary to predict the flows in each of the pipes of the network when the plants are operating at full capacity.
(a) Construct the system of linear equations that describes the situation, knowing that for each knot in the system, the inflows are equal to the outflows. Identify the variables used.
(b) Use an appropriate solution method to find the solution set of the system of linear equations without taking into account the context.
(c) Taking the context into account, what can be expected as throughput between the knots N1 and N2?
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