Chapter 14, Problem 55EP

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 ( $\text{ID}$ ) of the duct is $\text{D}=\text{9}.0\text{6}$ in, its average roughness is $0.00\text{59}$ in, and its total length is $\text{L}=\text{34}.0\text{ ft}$ . There are three elbows along the duct, each with a minor loss coefficient of $0.\text{21}$ . Literature from the hood manufacturer lists the hood entry loss coefficient as $\text{4}.\text{6}$ based on duct velocity. When the damper is fully open, its loss coefficient is $\text{1}.\text{8}$ . A squirrel cage centrifugal fan with a $\text{9}.0$ -in inlet is available. Its performance data fit a parabolic curve of the form $H_{available}=a{H}_0-a{\stackrel{\dot{}}{V}}^2$ , where shutoff head $H_0=\text{2}.\text{3}0$ inches of water column, coefficient $\text{a}=\text{8}.\text{5}0\times \text{l}{0}^{-6}$ inches of water column per ${\left(\text{SCFM}\right)}^2$ , available head $H_{available}$ is in units of inches of water column, and capacity $\stackrel{\dot{}}{V}$ is in units of standard cubic feet per minute $\left(\text{SCFMat 77}°F\right)$ . Estimate the volume flow rate in $\text{SCFM}$ through this ventilation system.

  FIGUREP 14—55E