6.1 Fan Laws, Airflow Dynamics & Total External Static Pressure

Fan Laws, Airflow Dynamics & Total External Static Pressure

Quick Reference: In HVAC air distribution, airflow ($CFM$), static pressure ($SP$), and fan power ($BHP$) are governed by the Affinitive Fan Laws. Standard air density is $0.075\text{ lb/ft}^3$ at sea level ($70^\circ\text{F}$, $29.92\text{ in. Hg}$). Air velocity ($V$) is derived from velocity pressure ($VP$) via the standard formula $V = 4005 \sqrt{VP}$. Total External Static Pressure (TESP) is the sum of the absolute static pressure measured at the supply plenum and return plenum: $\text{TESP} = |SP_{\text{supply}}| + |SP_{\text{return}}|$.

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1. The Three Fundamental Fan Laws

The fan laws (affinitive laws) predict performance changes in centrifugal blowers and axial fans when rotational speed ($RPM$), impeller diameter ($D$), or air density ($\rho$) changes. For a fixed fan diameter and constant air density, the three operational fan laws are:

Fan Law 1: Airflow vs. Fan Speed (Linear Relationship)

Volumetric airflow rate ($CFM$) varies directly and linearly with fan rotational speed ($RPM$):

$\frac{CFM_2}{CFM_1} = \frac{RPM_2}{RPM_1} \quad \implies \quad CFM_2 = CFM_1 \times \left( \frac{RPM_2}{RPM_1} \right)$

Fan Law 2: Static Pressure vs. Fan Speed (Square Relationship)

Static pressure ($SP$), velocity pressure ($VP$), and total pressure ($TP$) vary with the square of the fan speed ratio:

$\frac{SP_2}{SP_1} = \left( \frac{RPM_2}{RPM_1} \right)^2 = \left( \frac{CFM_2}{CFM_1} \right)^2 \quad \implies \quad SP_2 = SP_1 \times \left( \frac{RPM_2}{RPM_1} \right)^2$

Fan Law 3: Power vs. Fan Speed (Cubic Relationship)

Brake Horsepower ($BHP$) and electrical power consumption vary with the cube of the fan speed ratio (and cube of the airflow ratio):

$\frac{BHP_2}{BHP_1} = \left( \frac{RPM_2}{RPM_1} \right)^3 = \left( \frac{CFM_2}{CFM_1} \right)^3 \quad \implies \quad BHP_2 = BHP_1 \times \left( \frac{RPM_2}{RPM_1} \right)^3$

Fan Law Summary Ratios:
Speed Multiplier (x):      1.00    1.10 (+10%)    1.20 (+20%)    1.30 (+30%)
Airflow (CFM = x^1):       1.00    1.10 (+10%)    1.20 (+20%)    1.30 (+30%)
Static Pressure (SP = x^2): 1.00   1.21 (+21%)    1.44 (+44%)    1.69 (+69%)
Power Draw (BHP = x^3):    1.00    1.33 (+33%)    1.73 (+73%)    2.20 (+120%)

Pulley & Sheave Ratio Dynamics

For belt-driven commercial air handlers and packaged rooftop units, fan speed adjustments are made using adjustable pitch motor sheaves or replacement pulleys:

$D_{\text{motor}} \times RPM_{\text{motor}} = D_{\text{fan}} \times RPM_{\text{fan}}$

$RPM_{\text{fan}} = RPM_{\text{motor}} \times \left( \frac{D_{\text{motor}}}{D_{\text{fan}}} \right)$

Where $D_{\text{motor}}$ is the pitch diameter of the motor drive sheave, and $D_{\text{fan}}$ is the pitch diameter of the blower pulley.

Worked Example: Fan Law Calculations & Motor Loading

A commercial belt-driven air handler currently operates at $800\text{ RPM}$ with a $1.5\text{ HP}$ motor delivering $2,400\text{ CFM}$ against an external static pressure of $0.60\text{ in. w.c.}$ The measured operating brake horsepower is $1.20\text{ BHP}$. The commissioning engineer requires an increase in airflow to $2,760\text{ CFM}$ ($+15%$ increase).

1. Calculate Required Fan Speed ($RPM_2$): $RPM_2 = 800 \times \left( \frac{2760}{2400} \right) = 800 \times 1.15 = 920\text{ RPM}$

2. Calculate New Static Pressure ($SP_2$): $SP_2 = 0.60 \times (1.15)^2 = 0.60 \times 1.3225 = 0.7935\text{ in. w.c.}$

3. Calculate New Power Requirement ($BHP_2$): $BHP_2 = 1.20 \times (1.15)^3 = 1.20 \times 1.520875 = 1.825\text{ BHP}$

4. Motor Sizing Evaluation: The existing $1.5\text{ HP}$ motor has a full-load rating of $1.50\text{ BHP}$ (or $1.725\text{ BHP}$ assuming a standard $1.15$ service factor). Operating at $1.825\text{ BHP}$ will cause continuous motor overload, tripping the thermal overload or burning out windings. The motor must be upgraded to a $2.0\text{ HP}$ or $3.0\text{ HP}$ motor before increasing sheave pitch.

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2. Airflow Dynamics: Total, Static & Velocity Pressure

Air moving through ductwork exerts three distinct pressure components governed by Bernoulli's conservation of energy principle:

$TP = SP + VP \quad \iff \quad VP = TP - SP$

Air Velocity & Flow Rate Equations

At standard air density ($\rho = 0.075\text{ lb/ft}^3$, corresponding to dry air at $70^\circ\text{F}$ and $29.92\text{ in. Hg}$ barometric pressure), air velocity ($V$) in feet per minute (FPM) is derived from velocity pressure ($VP$) in inches water column (in. w.c.):

$V = 4005 \times \sqrt{VP}$

$VP = \left( \frac{V}{4005} \right)^2$

Once velocity is determined, volumetric flow rate ($Q$ or $CFM$) is calculated across the duct cross-sectional area ($A$ in square feet):

$CFM = V \times A = 4005 \times \sqrt{VP} \times \left( \frac{\text{Duct Width (in)} \times \text{Duct Height (in)}}{144} \right)$

Pitot Tube Duct Traverse (AMCA 204 / ASHRAE 111)

Because air velocity is not uniform across a duct—flowing faster in the center due to boundary layer wall friction—field airflow cannot be determined from a single centerline measurement. Technicians perform a Pitot Tube Traverse using equal-area grids or log-Tchebycheff spacing:

• Rectangular Ducts: Minimum of 16 to 24 traverse points divided into equal rectangular sub-areas (4×4 or 5×5 grid).
• Round Ducts: Minimum of two traverses at $90^\circ$ to each other, taking 6 to 10 points along each diameter.
• True Average Velocity: Average the square roots of the velocity pressures, not the raw velocity pressures: $V_{\text{avg}} = 4005 \times \left( \frac{\sum_{i=1}^n \sqrt{VP_i}}{n} \right)$

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3. Total External Static Pressure (TESP) Measurement

Total External Static Pressure is the primary diagnostic metric used to verify that an installed HVAC system can deliver design airflow without overheating, freezing the evaporator coil, or over-amping the blower motor.

Static Pressure Measurement Locations

   RETURN DUCTWORK                    AIR HANDLER / FURNACE                  SUPPLY PLENUM
 [Return Grille] ===> (Filter) ===> [Blower] ===> [Heat Exchanger / Coil] ===> [Supply Trunk]
                         |              |                       |
                      Port 1         (Blower)                 Port 2
                  Return Static                            Supply Static
                  (-0.35 in. wc)                           (+0.20 in. wc)

1. Furnace with External Cased Evaporator Coil:
   • Return Static ($SP_{\text{return}}$): Measure in the return drop between the air filter and the furnace blower cabinet entrance (negative pressure).
   • Supply Static ($SP_{\text{supply}}$): Measure in the supply transition between the top of the furnace heat exchanger and the bottom of the cased evaporator coil (positive pressure).
   • Note: If measuring external to the entire package (including cased coil), supply static is taken downstream of the coil in the supply plenum, and the coil pressure drop must be accounted for.
2. Modular Air Handler / Packaged Heat Pump (Internal Coil):
   • Return Static: In the return plenum immediately before the air handler cabinet inlet.
   • Supply Static: In the supply trunk approximately 1 to 2 feet downstream of the air handler discharge.

TESP Calculation Formula

$\text{TESP} = |SP_{\text{supply}}| + |SP_{\text{return}}|$

$\text{TESP} = SP_{\text{supply}} - SP_{\text{return}} \quad (\text{where } SP_{\text{return}} \text{ is a negative value})$

Example: If supply plenum static pressure is $+0.22\text{ in. w.c.}$ and return plenum static pressure is $-0.38\text{ in. w.c.}$, the Total External Static Pressure is: $\text{TESP} = |+0.22| + |-0.38| = 0.60\text{ in. w.c.}$

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4. Component Pressure Drops ($CPSC$)

When evaluating Available Static Pressure ($ASP$) for Manual D duct design, contractors must account for internal and external accessory pressure drops:

| Component | Typical Pressure Drop Range (in. w.c.) | Key Variables Influencing Loss | |---|---|---|---| | Dry DX Evaporator Coil | $0.15 - 0.25\text{ in. w.c.}$ | Fin density (FPI), face area, circuiting | | Wet DX Evaporator Coil (Dehumidifying) | $0.20 - 0.35\text{ in. w.c.}$ | Condensed water film bridges fin gaps ($+20%$ to $+40%$ vs. dry) | | Standard 1" Fiberglass Filter | $0.05 - 0.10\text{ in. w.c.}$ | Dust loading, low arrestance (MERV 2–4) | | High-Efficiency 1" Pleated Filter (MERV 11–13)| $0.20 - 0.40\text{ in. w.c.}$ | High restriction at standard $300-500\text{ FPM}$ face velocities | | Deep 4"–5" Media Filter (MERV 11–16) | $0.10 - 0.18\text{ in. w.c.}$ | Expanded surface area reduces face velocity and resistance | | Electric Resistance Heating Element | $0.03 - 0.08\text{ in. w.c.}$ | Kilowatt rack density, coil open-wire spacing | | Supply Diffusers / Registers | $0.03 - 0.05\text{ in. w.c.}$ | Grille damper position, blade throw configuration | | Return Filter Grille (including filter) | $0.15 - 0.25\text{ in. w.c.}$ | Grille free area ($A_k$), filter loading | | UV Germicidal / Electronic Air Cleaner | $0.02 - 0.06\text{ in. w.c.}$ | Lamp rack aerodynamic obstruction |

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5. Fan Motor Technologies: PSC vs. ECM

Modern residential and light commercial HVAC equipment utilizes two primary blower motor architectures with drastically different pressure-airflow responses:

Airflow (CFM)
  ^
  |  [Constant-Airflow ECM: Maintains CFM across rising static by ramping RPM]
  |  ------------------------------------
  |                                      \
  |  [PSC Motor: Airflow drops steeply as static increases]  \
  |  \\                                                       \
  |   \\                                                       \
  |    \\                                                       \
  +-------------------------------------------------------------------> Static Pressure (in. wc)
      0.2     0.4     0.6     0.8     1.0     1.2

Permanent Split Capacitor (PSC) Motors

• Operating Principle: Single-phase induction motor with fixed speed taps (Low, Med-Low, Med-High, High). Operates on a fixed rotor torque curve.
• Static Pressure Response: As duct static pressure rises (e.g., from a dirty filter or undersized ducts), blower speed drops, and volumetric airflow ($CFM$) declines rapidly.
• Consequences of High Static: In cooling mode, low CFM causes evaporator coil freeze-up and liquid refrigerant floodback to the compressor. In heating mode, low CFM trips the furnace high-limit switch.

Electrically Commutated Motors (ECM)

• Constant-Torque ECM (X13 / Endura Pro): Direct-current brushless motor with electronic commutation. Maintains fixed torque settings; airflow declines moderately with rising static pressure, but less severely than PSC.
• Constant-Airflow ECM (Variable Speed 2.0 / 3.0): Microprocessor-controlled feedback loop continuously monitors motor speed ($RPM$) and back-EMF (torque). As static pressure rises, the motor automatically increases speed and wattage to deliver constant programmed CFM up to its maximum design limit (typically $0.80 - 1.00\text{ in. w.c.}$).
• High Static ECM Trap: When static pressure exceeds $0.80\text{ in. w.c.}$, ECM blowers draw maximum electrical wattage, generate excessive aerodynamic noise, and may experience thermal failure of the electronic control module.

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6. System Effect Factors (SEF)

System Effect is the loss in fan performance resulting from poor aerodynamic inlet or outlet duct connections. Fan performance tables published by manufacturers (such as AMCA-certified ratings) are measured under ideal laboratory conditions with long, straight duct runs.

Common Field System Effect Causes

1. Abrupt Discharge Elbows: Installing a $90^\circ$ mitered elbow immediately at the blower discharge creates high localized turbulence and prevents static pressure regain. AMCA standard 200 recommends a minimum of $2.5\text{ to }4.0\text{ equivalent duct diameters}$ of straight discharge duct to achieve $100%$ effective recovery.
2. Eccentric Inlets: Sharp bends or offsets entering the blower inlet induce pre-rotation (swirl), cutting fan capacity by $15%$ to $30%$.
3. Inlet Obstructions: Placing filters, structural joists, or sharp transitions closer than one fan inlet diameter to the blower suction opening.