Figura del problema $8$In the intake structure whose geometry is shown in the figure, the extractions from the reservoir are controlled by two service gates that block two orifices, each $1$ meter wide and within the indicated range of reservoir levels. Assuming negligible energy loss at the screen and free discharge towards the tunnel:

a$)$ Calculate the height

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h that the orifices should have so that, with the minimum level in the reservoir and the gates fully open, the flow rate extracted by the intake is $15$ m$^3/$s$.$

b$)$ Given this height, calculate what the gate opening should be to discharge the same flow rate when the level in the reservoir is at its maximum.