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Unformatted text preview: PROBLEM 4.” 4.11 As shown in Fig. P.4.11, air with a volumetric flow rate of 15,000 ft3/rnin enters an
air-handling unit at 35°F, 1 arm. The air-handling unit delivers air at 80°F, 1 arm to a
duct system with three branches consisting of two 26-in.-diameter ducts and one 50-in.
duct. The velocity in each 26-in. duct is 10 ft/s. Assuming ideal gas behavior for the air:
determine at steady state (a) the mass flow rate of air entering the air-handlin unit, in 11313. (b) the volumetric flow rate in each 26-in. duct, in ft /min. (c) the velocity in the 50-in.duct, in ft/s. T2 : T3 = T4 = 80°F
D2=D3=26 in.
V2=V3=10 ft/S Air handling unit .............. P1=P2 2P3 =P4 =1atm
T, = 35°F
(AV); = 15,000 ft3/min Fig. P.4.11 KNOWN: At steady state, air enters an air-handling unit and exits from three ducts in an
attached duct system FIND: Determine the mass flow rate of air entering the air handling unit; in lb/s; the
volumetric flow rate in each 26-in. duct, in mein; and velocity in the 50-in.duct, in ft/s. SCHEMATIC AND GIVEN DATA:
See Figure P.4.11 ENGINEERING MODEL:
(1) The control volume shown on the schematic is at steady state.
(2) The air behaves as an ideal gas. PROBLEM 4.1: (Can'lfnued) ANALYSIS: _
(a) Determine the mass flow rate of air entering the air handling unit, in lb/s, as follows:
f“ n] lbf
15000—_— (latm) 14 72_ _ 2 _
"'1‘ Z (“)1 = (AER = [ ftbe 1 tin. 1:? 12:: ' 20 05— F—
v a m s
' ‘ ——1545 (495°R)
28.97 lb-° R (b) Determine the volumetric flow rate in each 26411. duct, in ft3/min, as follows: D 2 ' ‘ 2 2 ' 3
(AV)2 =(AV)3 = L 2 V2 = L6”) [10—125] ”T 2 60? =2212. 25t— ‘—
4 4 5 144m. 1mm min (c) Determine the velocity in the 50-in.duct, in ft/s, as follows:
dmn . . . . dt =0=m1—m2 —m3 —m4 3
[2212 23+ (latm) 14 711% 2 m _ m (AV)2 _ (AV)2 p2 mm in} 144111 1111111 2 71113 2— 3— _—‘—:"—-—4_—__——2——'—_ - — RT 1 tm 1ft 60
V2 2 l__545 ft- lbf (54010 a S 3
28.97 1b-° R
m,— — m1— m2— m3 =20. 05—3— 2(2. "Ill—b] =14. 631t-J
s s
”'14 = (AV)!
v4
[14 631:][_ 1545 ft 1be(5 40 R)
M4124 mil-T4 - 28. 97 lb R latm ft ‘___ V4 _ =- '— — _.146 —' ‘A 7:132 _ . 7:50'in.2 E 5
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I. A Card-r5! Vo‘U'IMP eh;!b$"n§I
Helium
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