When fermentation units are operated with high aeration rates, significant amounts of water can be evaporated into the air passi
ng through the fermentation broth. Since fermentation can be adversely affected if water loss is significant, the air is humidified before being fed to the fermenter. Sterilized ambient air is combined with steam to form a saturated air–water mixture at 1 atm and 90°C. The mixture is cooled to the temperature of the fermenter (35°C), condensing some of the water, and the saturated air is fed to the bottom of the fermenter. For an air flow rate to the fermenter of 10 L/min at 35°C and 1 atm, estimate the rate at which steam must be added to the sterilized air and the rate (kg/min) at which condensate is collected upon cooling the air–steam mixture.
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Answer
given,
a = 2 t - 10
velocity function
we know,
integrating both side
v = t² - 10 t + C
at t = 0 v = 3
so, 3 = 0 - 0 + C
C = 3
Velocity function is equal to v = t² - 10 t + 3
Again we know,
integrating both side
now, at t= 0 s = -4
C = -4
So,
Position function is equal to