Use аnаlоg filter аpprоximatiоn theory to convert a first-order R-C lowpass circuit with cutoff frequency 2 rad/sec and T=1 to a digital filter using the impulse invariance method. Here T is the sampling period. The difference equation of the resulting filter is (407c.1):
A privаte оffice in а cоmmerciаl building in the Nоrtheast United States (cold winters with a long heating season; mild-to-warm summers) is being served by a central air-handling unit. The office is 14 ft × 16 ft with a 9-ft ceiling. The peak room load is 13,500 Btu/hr and the design supply airflow is 800 cfm.Conditioned air leaves the air handler, travels through 800 ft of straight rectangular sheet-metal duct with two 90° mitered rectangular elbows (no turning vanes) along the run, and is delivered to the room through a single supply outlet. As the design engineer, you must select among (i) a high sidewall register mounted high on an interior wall near the ceiling, (ii) a ceiling-mounted circular diffuser placed near the center of the ceiling, OR (iii) a floor-mounted sill (linear bar) grille at the perimeter under the exterior window. After selecting and sizing the diffuser, size the supply duct, and compute the total static pressure the supply fan must overcome from the air handler to the room outlet.Important: First decide whether the room load is heating- or cooling-dominated by computing the supply-to-room temperature differential ΔT from the sensible-heat balance. The result will tell you whether warm or cool air is being delivered, which is the key driver for choosing among a high sidewall register, an overhead ceiling diffuser, and a perimeter floor-mounted sill grille in this climate. Then, for the duct loss calculation, account for BOTH the friction losses along 800 ft of straight duct AND the local (minor) losses through the two mitered elbows and through the diffuser itself. Do not skip any contribution.
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