10.3 Hood Airflow Equations, Entry Losses, and Hood Static Pressure

Hood Airflow Equations, Entry Losses, and Hood Static Pressure

Selecting the hood and the capture velocity fixes the design intent. Converting that intent into a specified exhaust volume, an entry loss, and a hood static pressure is what makes the system buildable and testable — and hood static pressure is the single field measurement that tells you whether the hood is still moving design airflow.

1. Volumetric Airflow Equations (Q) by Hood Geometry

The ACGIH Industrial Ventilation: A Manual of Recommended Practice for Design establishes empirical and analytical equations relating the required volumetric airflow rate (Q, in cubic feet per minute, cfm), capture velocity (V_c, in feet per minute fpm), hood face area (A, in square feet, ft²), and capture distance (x, in feet, ft).

   +-------------------------------------------------------------------------+
   |                  HOOD AIRFLOW EQUATION GEOMETRIES                       |
   +-------------------------------------------------------------------------+
   |                                                                         |
   |  PLAIN OPEN HOOD:                 FLANGED HOOD (25% Savings!):          |
   |                                                                         |
   |         /---------+                      +-------+                      |
   |        /  Area A  |                      |FLANGE |                      |
   |       /           |                      +-------+                      |
   |  <===|   DUCT     |                 <===|  DUCT  |                      |
   |       \           |                      +-------+                      |
   |        \          |                      |FLANGE |                      |
   |         \---------+                      +-------+                      |
   |               <--- x --->                      <--- x --->              |
   |                     * Contaminant                    * Contaminant      |
   |                                                                         |
   |      Q = Vc (10x^2 + A)               Q = 0.75 Vc (10x^2 + A)           |
   +-------------------------------------------------------------------------+

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2. Hood Aerodynamics, Entry Losses, and Hood Static Pressure (SPh)

Total Pressure, Static Pressure, and Velocity Pressure

Airflow through a ventilation system is governed by Bernoulli's conservation of energy principle, expressed in terms of fluid pressures measured in inches of water gauge (extin. w.g.) or Pascals (extPa):

$TP = SP + VP$

• Total Pressure (TP): The total aerodynamic energy per unit volume in the fluid stream.
• Static Pressure (SP): The potential energy exerted equally in all directions against the interior duct walls (measured perpendicular to flow). In an exhaust system upstream of the fan, SP is always negative relative to atmospheric pressure.
• Velocity Pressure (VP): The kinetic energy of air motion in the direction of flow. VP is always positive and cannot be negative:

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

(where V is velocity in fpm, VP is in in. w.g., and air density is standard 0.075 lb/ft³).

Physics of Hood Entry Loss (he)

In the ambient room outside the hood, air is at rest: TProom = 0, SProom = 0, and VProom = 0.

To move air into the duct, the exhaust fan must supply energy to:

1. Accelerate the air from zero velocity to the duct velocity (Vd), creating velocity pressure (VPd).
2. Overcome turbulent frictional losses and vena contracta vortex shedding (he) as air converges into the hood mouth.

   +-------------------------------------------------------------------------+
   |             VENA CONTRACTA AND HOOD ENTRY LOSS MECHANICS               |
   +-------------------------------------------------------------------------+
   |                                                                         |
   |     PLAIN DUCT END (Sharp 90° Edge):                                    |
   |       Air streamlines cannot make sharp 90° turns. Flow separates from  |
   |       the rim, contracting into a narrow jet (Vena Contracta) with      |
   |       massive turbulent wake eddies. High energy loss! (Fh = 0.93)       |
   |                                                                         |
   |         Duct Wall   ------------------------+                           |
   |                                 Turbulent   |  Flow streamlines         |
   |                              ( ( ( Eddies   |    |                      |
   |          <=================== ( ( (         |   /                       |
   |          <=================== ( ( (         |  <---                     |
   |                              ( ( ( Eddies   |   \                       |
   |         Duct Wall   ------------------------+    |                      |
   |                                                                         |
   |     BELLMOUTH / TAPERED HOOD (Smooth Transition):                       |
   |       Streamlines follow smooth curved surface. No flow separation.     |
   |       Near-zero turbulence! (Fh = 0.04 - 0.15)                          |
   |                                                                         |
   |         Duct Wall   -------------\                                      |
   |                                   \   Smooth streamlines                |
   |          <=========================)  <----------------                 |
   |          <=========================)  <----------------                 |
   |                                   /                                     |
   |         Duct Wall   -------------/                                      |
   +-------------------------------------------------------------------------+

The hood entry loss (he) is directly proportional to the duct velocity pressure (VPd):

$h_e = F_h \times VP_d$

Where Fh is the dimensionless hood entry loss coefficient (determined by hood entry geometry).

Hood Static Pressure (SPh) Master Equation

Hood static pressure (SPh), measured downstream of the hood entrance (typically 1 to 3 duct diameters into the straight duct), represents the total suction energy required to accelerate the air and overcome entrance turbulence:

$SP_h = -VP_d - h_e = -VP_d - (F_h \cdot VP_d) = -(1 + F_h)VP_d$

$\mathbf{|SP_h| = (1 + F_h)VP_d}$

Dimensionless Entry Loss Coefficients (Fh) and Coefficients of Entry (Ce)

The Coefficient of Entry (Ce)

The Coefficient of Entry (Ce) is the ratio of the actual airflow entering the hood to the theoretical airflow that would occur if there were zero turbulent friction losses for the same static pressure drop:

$C_e = \sqrt{\frac{VP_d}{|SP_h|}} = \sqrt{\frac{VP_d}{(1 + F_h)VP_d}} = \mathbf{\frac{1}{\sqrt{1 + F_h}}}$

Determining Volumetric Flow (Q) from Static Pressure (SPh)

In field practice, measuring static pressure (SPh) with a simple static pressure tap and U-tube manometer or Magnehelic gauge is faster, cheaper, and less prone to clogging than traversing dusty ducts with a Pitot tube. Volumetric flow rate is calculated directly:

$V_d = 4005 \sqrt{VP_d} = 4005 \sqrt{C_e^2 \cdot |SP_h|} = 4005 \cdot C_e \sqrt{|SP_h|}$

$\mathbf{Q = 4005 \cdot C_e \cdot A_d \sqrt{|SP_h|}}$

(where Q is in cfm, Ad is duct cross-sectional area in ft², and |SPh| is in in. w.g.).

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3. Worked Step-by-Step Calculation Examples

Worked Example 9.1.1: Sizing Airflow for Flanged vs. Plain Exterior Hood

Problem: An exterior exhaust hood must capture solvent vapors evaporating from a parts cleaning bench. The contaminant source is located at a distance x = 10 inches (0.8333 ft) from the hood face. The hood opening is rectangular with dimensions 12 in × 6 in (Area A = 0.50 ft²). The required capture velocity at the solvent source is Vc = 120 fpm.

1. Calculate the required volumetric airflow rate (Qplain) if the hood is a freestanding plain open duct.
2. Calculate the required volumetric airflow rate (Qflanged) if a standard perimeter flange is added.
3. Determine the percentage airflow and energy savings achieved by flanging the hood.

Solution Steps:

1. Calculate airflow for Plain Open Hood (Q = Vc [10 x² + A]): $x = 10\text{ in} = \frac{10}{12} = 0.8333\text{ ft}, \quad x^2 = (0.8333)^2 = 0.6944\text{ ft}^2$ $Q_{\text{plain}} = 120\text{ fpm} \times [(10 \times 0.6944) + 0.50\text{ ft}^2]$ $Q_{\text{plain}} = 120 \times [6.944 + 0.50] = 120 \times 7.444 = 893.3\text{ cfm} \approx 893\text{ cfm}$

2. Calculate airflow for Flanged Hood (Q = 0.75 · Vc [10 x² + A]): $Q_{\text{flanged}} = 0.75 \times 893.3\text{ cfm} = 670.0\text{ cfm} \approx 670\text{ cfm}$

3. Calculate airflow savings: $\Delta Q = 893.3 - 670.0 = 223.3\text{ cfm} \quad \left(\frac{223.3}{893.3} \times 100 = 25.0\%\right)$

Result: Adding a flange reduces the required exhaust flow from 893 cfm down to 670 cfm—a 25% reduction in required airflow and fan operating power while delivering the exact same 120 fpm capture velocity at the solvent source.

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Worked Example 9.1.2: Hood Static Pressure, Entry Loss, and Ce Calculation

Problem: A tapered exhaust hood (60° included angle, Fh = 0.15) connects to an 8-inch diameter round duct (D = 8 in = 0.6667 ft, Ad = π · (8/24)² = 0.3491 ft²). The LEV system conveys Q = 1400 cfm of standard air.

1. Calculate the duct velocity (Vd) and velocity pressure (VPd).
2. Calculate the hood entry loss (he) in inches of water gauge.
3. Determine the theoretical hood static pressure (SPh).
4. Calculate the Coefficient of Entry (Ce).

Solution Steps:

1. Calculate duct velocity (Vd) and velocity pressure (VPd): $V_d = \frac{Q}{A_d} = \frac{1400\text{ cfm}}{0.3491\text{ ft}^2} = 4010.3\text{ fpm} \approx 4010\text{ fpm}$ $VP_d = \left(\frac{V_d}{4005}\right)^2 = \left(\frac{4010.3}{4005}\right)^2 = (1.0013)^2 = 1.003\text{ in. w.g.}$

2. Calculate hood entry loss (he = Fh × VPd): $h_e = 0.15 \times 1.003\text{ in. w.g.} = 0.1505\text{ in. w.g.}$

3. Calculate Hood Static Pressure (SPh): $SP_h = -(1 + F_h)VP_d = -(1 + 0.15) \times 1.003 = -1.15 \times 1.003 = -1.153\text{ in. w.g.}$

4. Calculate Coefficient of Entry (Ce): $C_e = \frac{1}{\sqrt{1 + F_h}} = \frac{1}{\sqrt{1.15}} = \frac{1}{1.07238} = 0.9325$ Cross-check using pressures: Ce = √(VPd/|SPh|) = √(1.003/1.153) = √(0.8699) = 0.9327.

Result: The duct velocity is 4010 fpm, hood entry loss is 0.151 in. w.g., hood static pressure is -1.15 in. w.g., and the coefficient of entry is 0.933.

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Worked Example 9.1.3: Volumetric Airflow Determination from Field SPh Measurement

Problem: During a routine industrial hygiene compliance audit of a plating line, an IH measures a static pressure of SPh = -1.44 in. w.g. at a test tap located 2 duct diameters downstream of a flanged slot hood (Ce = 0.82). The exhaust duct has an inside diameter of 10 inches (Ad = 0.5454 ft²). Calculate the actual volumetric flow rate (Q) passing through the LEV branch.

Solution Steps:

1. Identify parameters: Ce = 0.82, Ad = 0.5454 ft², |SPh| = 1.44 in. w.g.

2. Apply the Master Flow Rate Equation (Q = 4005 · Ce · Ad √(|SPh|)): $\sqrt{|SP_h|} = \sqrt{1.44} = 1.20$ $Q = 4005 \times 0.82 \times 0.5454 \times 1.20$ $Q = 4005 \times 0.82 \times 0.65448 = 2149.4\text{ cfm} \approx 2150\text{ cfm}$

3. Calculate Duct Velocity (Vd) to verify: $V_d = \frac{Q}{A_d} = \frac{2149.4\text{ cfm}}{0.5454\text{ ft}^2} = 3941\text{ fpm}$ $VP_d = \left(\frac{3941}{4005}\right)^2 = (0.9840)^2 = 0.9683\text{ in. w.g.}$ Verify Ce: Ce = √(VPd/|SPh|) = √(0.9683/1.44) = √(0.6724) = 0.820.

Result: The measured static pressure of -1.44 in. w.g. confirms an active branch airflow of 2150 cfm.