For the duct system and fan of Prob. 14–55E, partially closing the damper would decrease the flow rate. All else being unchanged, estimate the minor loss coefficient of the damper required to decrease the volume flow rate by a factor of 3.

Data from Problem 14–55E

A local ventilation system (a hood and duct system) is used to remove air and contaminants produced by a welding operation (Fig. P14–55E). The inner diameter (ID) of the duct is D = 9.06 in, its average roughness is 0.0059 in, and its total length is L = 34.0 ft. There are three elbows along the duct, each with a minor loss coefficient of 0.21. Literature from the hood manufacturer lists the hood entry loss coefficient as 4.6 based on duct velocity. When the damper is fully open, its loss coefficient is 1.8. A squirrel cage centrifugal fan with a 9.0-in inlet is available. Its performance data fit a parabolic curve of the form H_available  = H₀ – aV̇², where shutoff head H₀ = 2.30 inches of water column, coefficient a = 8.50 × 10^–6 inches of water column per (SCFM)², available head H_available is in units of inches of water column, and capacity V̇ is in units of standard cubic feet per minute (SCFM, at 77°F). Estimate the volume flow rate in SCFM through this ventilation system.

FIGURE P14–55E

Transcribed Image Text:

Hood 1 Fan N 22 Damper Z1