# EWEEK PROBLEM OF THE DAY: WEDNESDAY

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Systems engineers work in many different engineering fields. They often serve as both project manager and chief engineer. In mechanical engineering in particular, systems engineers need to ensure individual sub-systems and components of a large project all work together to perform the overall desired function. Many professionals in mechanical engineering work in HVAC (heating, ventilation and air conditioning). These systems are essential to keeping indoor spaces safe and comfortable.

An outdoor air ventilation system is used to regulate the breathing zone outdoor airflow (Vbz) in a space. In other words, it ensures that the amount of outdoor air, measured in cubic feet per minute (cfm), in a space meets a particular standard based on the function of the space. These standards are set by the American Society of Heating, Refrigerating and Air-Conditioning Engineers (ASHRAE). As the formula shows, HVAC engineers must consider the square footage and the number of people occupying a space when determining the total amount of outdoor air needed.

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3.1 Suppose MATHCOUNTS hires an HVAC systems engineer to install an outdoor air ventilation system in our office building. The figure shows the dimensions of the MATHCOUNTS conference room. According to ASHRAE standards for office buildings, Rp = 5 cfm and Ra = 0.06 cfm. Based on this, what Vbz should the ventilation system maintain in order for this conference room to accommodate the MATHCOUNTS staff of 11? Express your answer as a decimal to the nearest hundredth.

3.2 Ventilation plays a key role in air conditioning systems. By using fans, the systems prevent stagnation and ensure that air continues to circulate. In MATHCOUNTS’ system, the fans are currently operating at a speed of 1500 revolutions per minute (rpm), producing an air flow rate of 370 cfm. This rate, however, is determined to be about 20% below the acceptable rate for air circulation. Given that the change in speed of the fan’s propeller is directly proportional to the change in air flow rate of a fan, at what speed, in revolutions per minute, should the fans in the MATHCOUNTS’ system operate for the air to flow at a rate that is 20% greater than the current air flow rate?

3.3 Later, an HVAC systems engineer who examines the full system notes that the fan is set to operate at 2000 rpm but determines that the static pressure (the amount of pressure needed by a fan to push and pull air through ductwork) needs to be reduced by lowering the fan speed to 1850 rpm. If the square of the ratio of the new propeller speed to the old propeller speed is equal to the ratio of the new static pressure to the old static pressure, by what percent will the static pressure need to be reduced? Express your answer to the nearest whole percent.