A $15$MW geothermal power plant is being considered at a site where geothermal water at $250$ C $($Degree Celcius$)$ is available. Geothermal water is to be flashed into a chamber to a lower pressure where part of the water evaporates. The liquid is returned to the ground while the vapor is used to drive the steam turbine. The pressures at the turbine inlet and the turbine exit are to remain above $150$ kPa and $8$ kPa, respectively. High pressure flash chambers yield a small amount of steam with high exergy whereas lower$-$pressure flash chambers yield considerably more steam but at a lower exergy. By trying several pressures, determine the optimum pressure of the flash chamber to maximize the power production per unit mass flow rate of geothermal water withdrawn. For each pressure, design the Rankine cycle and determine the thermal efficiency assuming $15$ percent of the power produced is used to drive the pumps and other auxiliary equipment. Plot results against the pressure of flash chambers