A power plant is using a regenerative Rankine cycle as shown in Figure Q$4,$

operating at a boiler pressure of $4$MPa and a maximum temperature of $450C.$

The mass flow rate of water into the boiler is $10k\frac{g}{s}.$ The inlet into both pump $1$

and pump $2$ is a saturated liquid. Superheated steam for regeneration is bled

from the turbine at $500$kPa, and mixed with the water leaving pump $1$ in an open

feedwater heater $($OFWH$).$ The power plant uses water from a nearby river as

cooling liquid for the condenser. The river water can be assumed to have a

constant temperature of $15C.$

$($iii$)$ Determine the dryness fraction at the outlet of the turbine.

$($iv$)$ Calculate the mass flow rate of steam removed from the turbine at point $6$

entering the OFWH in $k\frac{g}{s}.$

$($v$)$ Calculate the net power output and the thermodynamic efficiency of the

power plant.

You discover a leak in the regeneration system, which loses $10\%$ of the steam

that was bled from the turbine. The leak is in the pipework before the feedwater

heater as indicated in figure Q$4.$ Fixing the leak is not immediately possible, so

you make some adjustments to the cycle to keep it operating:

First, you add water at the inlet of pump $1$ to make up for the steam lost at the

leak. The water added can be assumed to be saturated liquid.

Second, you adjust the power of pump $1$ such that the fluid entering pump $2$ is

a saturated liquid.

$($vi$)$ To what power do you adjust pump $1$ for this scenario?

Give your answer in kW$.$

The leak is getting worse, and to be able to repair the leak you close the pipework

between the turbine and the feedwater heater. In this new scenario, no more

steam is bled from the turbine, and no more steam enters the feedwater heater.

$($vii$)$ Without doing any calculations, explain how this influences the efficiency

and the net power output of the cycle.

$($i$)$ Draw a T$-$s diagram of the cycle.

$($ii$)$ Choose a suitable condenser pressure for the cycle, explaining your

choice. Use your chosen value for all following questions.