Air is constantly being recirculated throughout the ME Building. In the summer t

Question

Air is constantly being recirculated throughout the ME Building. In the summer that air is also cooled, using chilled water supplied by the South Power Plant. A schematic of such a system is shown below, along with photographs of actual hardware housed in the ME Building (its location is top secret). SP-c: Consider first air flowing through the fan/blower. It enters the fan from a plenum, where its velocity is essentially zero, and exits into a rectangular duct whose dimensions are 24 times 36 inches. The target flow rate is 800 scfm (scfm - standard cubic feet per minute, with standard implying 77 F and 1 standard atm). While flowing through the blower the air temperature can be approximated as constant; the pressure rises by 2 inches of water. What is the air velocity in the duct? Report your answer in ft/s. What is the air mass flow rate in lb m/sec? What fan power is required to provide this flow? Report your answer in hp. If the fan is 90 % efficient, what motor power is required? Again, report your answer in hp.

Explanation / Answer

I am not used to working with these units so i will just give the formulae. We assume that the potential energy remains constant. Since the temperature is constant in the blower, the increase in kinetic energy is due to the increase in pressure. From bernoulli's equation we have p1-p2= 1/2 pho v2^2- 1/2 pho v1^2, Since v1=0, you can get v2 from here. pho is the fluid density The mass flow rate will be given by volume flow rate* denisty. The power required is dE/dt, but nothing about time is given here. The final volumetric mass flow, is A.v where A is the area of cross section of the pipe. You can see http://en.wikipedia.org/wiki/Centrifugal_fan to find out how to find out the power

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