Engineering Manual o.. - HVAC.Amickracing

BUILDING AIRFLOW SYSTEM CONTROL APPLICATIONSFAN LAWSFan laws (Table 1) are simple and useful when dealing withchanging conditions. Three important laws deal with speedchanges:1. Airflow varies directly with the fan speed. For example,doubling the fan speed (rpm) doubles the airflow (cfm)delivery.2. Static pressure varies as the square of the fan speed. Forexample, doubling the fan speed (rpm) develops fourtimes the static pressure (in. wc).3. Power varies as the cube of the fan speed. For example,doubling the fan speed (rpm) requires eight times the fanpower (hp).Table 1. Fan LawsWhenWhenVariable Speed Changes Density ChangesAirflowVaries DIRECT withSpeed RatioCFM2 =CFM1( RPM2)2RPM1Does Not ChangeBrake horsepower (bhp) is the actual horsepower requiredto drive the fan.bhp= Theoretical hp ÷ Fan efficiency= (cfm x FTP) ÷ (6356 x Fan efficiency)The brake horsepower is always larger than the theoreticalhorsepower due to inefficiencies. The actual brake horsepowerof the fan can be determined only by testing.DUCT SYSTEM CURVESFan unit duct systems have a certain amount of friction, orresistance, to the flow of air. Once this resistance of the ductsystem is known for a specific volume of airflow, a curve canbe drawn based on the relationship:P2P1 = ⎝ ⎛ cfm2cfm1⎠ ⎞ 2This formula is merely another way of stating that pressure(P) changes as the square of the airflow (cfm).The system curve (also called system resistance, ductresistance, or system characteristic) is similar to Figure 6.PressureFAN HORSEPOWERVaries with SQUARE ofSpeed Ratio2 RPM2P2 = P1( RPM1)Varies with CUBE ofSpeed RatioHorsepower3 RPM2HP 2 = HP1( RPM1)The theoretical horsepower (hp) required to drive a fan isthe horsepower required if there were no losses in the fan (100percent efficiency). The horsepower formula is:Theoretical hp = (cfm x FTP) ÷ 6356Varies DIRECTwith Density RatioD2P2 = P1( D1)Varies DIRECTwith Density RatioD2HP 2 = HP1( D1)STATIC PRESSURE (∆P) IN. WC2.42.22.01.81.61.41.21.00.80.60.40.20010,000 20,000 30,000AIRFLOW CFMC2641Fig. 6. System Curve.Where:cfm = Quantity of air6356 = A constant for English unitsFTP = Fan total pressure.FAN CURVE AND SYSTEM CURVE COMPARISONIn order to deliver the required air quantity, a fan must beselected that can overcome the duct resistance. However,because of dampers repositioning and other equipment changes,resistance of the duct may change. The results of such conditionscan be seen in Figure 7.ENGINEERING MANUAL OF AUTOMATIC CONTROL254