A sphere of diameter 2 mm Falls 150 mm into 20 seconds in a viscous liquid. The density of the sphere is 7500kg/m37500kg/m3 and liquid is 900kg/m3900kg/m3. Find coefficient of viscosity of the liquid.

 A sphere of diameter 2 mm Falls 150 mm into 20 seconds in a viscous liquid. The density of the sphere is 7500kg/m3$7500kg/m^3$ and liquid is 900kg/m3$900kg/m^3$. Find coefficient of viscosity of the liquid.

Solution:-

 Given:-

Diameter of sphere, d=2mm=2×10−3m$d=2mm=2\times {10}^{-3}m$

Distance travelled by sphere =150mm=0.15m

Time taken, t=20seconds

Velocity of sphere, V=0.1520=0.0075m/s$V={\displaystyle \frac{0.15}{20}}=0.0075m/s$

Density of sphere, ρS=7500kg/m3${\rho }_S=7500kg/m^3$

Density of fluid, ρF=900kg/m3${\rho }_F=900kg/m^3$

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μ=gD218V[ρS−ρF]$\mu ={\displaystyle \frac{g{D}^2}{18V}}[{\rho }_S-{\rho }_F]$

μ=9.81×[2×10−3]218×0.0075[7500−900]$\mu ={\displaystyle \frac{9.81\times [2\times {10}^{-3}{]}^2}{18\times 0.0075}}[7500-900]$

μ=9.81×4×10−6×660018×0.0075$\mu ={\displaystyle \frac{9.81\times 4\times {10}^{-6}\times 6600}{18\times 0.0075}}$

μ=1.917NS/m2=1.917NS/m2×10$\mu =1.917NS/m^2=1.917NS/m^2\times 10$ poise

μ=19.17$\mu =19.17$ poise