Evaluate the Reynold’s number at terminal velocity in air at 20oC, of a spherical dust particle of radius 1.0 X 10-5m and density 2.0 X 10-3Kgm-3.
Gives
ρair=1.2kg/m3\rho_{air}=1.2kg/m^3ρair=1.2kg/m3
ηair=1.8×10−5Nsec/m2\eta_{air}=1.8\times10^{-5}Nsec/m^2ηair=1.8×10−5Nsec/m2
d=1.0×10−5m1.0\times10^{-5}m1.0×10−5m
ρdust=2.0×10−3kgm−3\rho_{dust}=2.0\times10^{-3}kgm^{-3}ρdust=2.0×10−3kgm−3
Vt=2r2(ρ−σ)9ηgV_t=\frac{2r^2(\rho-\sigma)}{9\eta}gVt=9η2r2(ρ−σ)g
Vt=2×1×10−5×(1.2−0.002)9×1.8×10−5×9.8V_t=\frac{2\times1\times10^{-5}\times(1.2-0.002)}{9\times1.8\times10^{-5}}\times9.8Vt=9×1.8×10−52×1×10−5×(1.2−0.002)×9.8
Vt=1.44m/secV_t=1.44m/secVt=1.44m/sec
Reynold's number
R=ρvcdηR=\frac{\rho v_c d}{\eta}R=ηρvcd
Put value
R=1×10−5×2.0×10−3×1.441.8×10−5R=\frac{1\times10^{-5} \times2.0\times10^{-3}\times1.44}{1.8\times10^{-5}}R=1.8×10−51×10−5×2.0×10−3×1.44
R=1600R=1600R=1600
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