Basic Calculations for Occupational Safety and Environmental Health Professionals - Mathematics and Statistics for the Environment - page 419

Hood entry losses normally occur at the hood slots and at the entrance to the duct, due to the vena
contracta formed. The most narrowed portion of the vena contracta is usually found about one-half
duct diameter inside the duct or plenum. The hood static pressure is the sum total of the acceleration
and all losses from the hood face to the point of measurement in the duct. Head loss is
H e = K × VP d × d
where K is the hood entry loss factor.
Hood entry loss factors have been estimated over the years and have been reported in the litera-
ture for many types of hoods, including lab fume hoods. Three types of hoods are the enclosing,
capture (active, external), and receiving (passive, often canopy type hood).
■ EXAMPLE 15.11
Problem: What is the hood entry loss ( H e ) for a laboratory fume hood when the average velocity
pressure in the duct is 0.30 in. wg? Assume K = 2.0 and d = 1.
Solution:
H e = K × VP d × d = 2.0 × 0.30 × 1 = 0.60 in. wg
The area approach is used too determine Q (flow) for capture hoods. Basically, air approaches
from all directions toward the source of negative pressure. Imagine a three-dimensional sphere
around the end of a small, plain duct hood. Air molecules don't know if they are in the front, to the
side, or to the back of the opening. All they know is that they are experiencing a big push to get over
to that spot of negative pressure. The velocity of air moving toward the opening is equal at all points
on the surface of the sphere. The surface area of a sphere is given by
A = 4π x 2
Knowing the area and the desired capture velocity at x , we can estimate the volume flow rate from
Q = V × A.
■ EXAMPLE 15.12
Problem: Air enters an ideal 4-in. plain duct hood. What is the required volume flow rate for capture
6 inches in front of the hood if we need V c = 100 fpm?
Solution:
Q = V c × A = 100 × 4π(0.5 ft) 2 = 315 cfm
where A = 4π x 2 ; 6 in. = 0.5 ft.
15.6.5.6 Fans
Types of fans include the centrifugal (forward curved, backward inclined, radial) and axial.
15.6.5.6.1 Fan Curves
Fan characteristic curves plot volume flow rate Q against static pressure, horsepower, noise, and
ef iciency.
15.6.5.6.2 Fan Specifications
Fans are specified by pressure and flow rate—the system operating point (SOP). The pressure is
found across the fan—at the inlet and outlet of the fan in the ductwork.