A 0.6 m diameter household fan takes air in at 98 kPa, 20°C and delivers it at 105 kPa, 21°C with a velocity of 1.5 m/s. What are the mass flow rate (kg/s), the inlet velocity and the outgoing volume flow rate in m ^{3} / s?
Question 4.18: A 0.6 m diameter household fan takes air in at 98 kPa, 20°C ...
Continuity Eq. \dot{ m }_{ i }=\dot{ m }_{ e }= A V / v
Ideal gas v = RT/P
Area : A =\frac{\pi}{4} D ^{2}=\frac{\pi}{4} \times0.6^{2}=0.2827 m ^{2}
\dot{ V }_{ e }= A V _{ e }=0.2827 \times 1.5= 0 . 4 2 4 1 \mathrm { m } ^ { 3 } / \mathrm { s }
v _{ e }=\frac{ RT _{ e }}{ P _{ e }}=\frac{0.287 \times(21+273)}{105}=0.8036 m ^{3} / kg
\dot{ m }_{ i }=\dot{ V }_{ e } / v _{ e }=0.4241 / 0.8036= 0 . 5 2 8 kg / s
AV _{ i } / v _{ i }=\dot{ m _{ i }}= AV _{ e } / v _{ e }
V _{ i }= V _{ e } \times\left( v _{ i } / v _{ e }\right)= V _{ e } \times \frac{ RT _{ i }}{ P _{ i } v _{ e }}= 1.5 \times \frac{0.287 kJ / kg – K \times(20+273) K }{98 kPa \times 0.8036 m ^{3} / kg }=1.6 m / s
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