Question

A 11-mm-diameter plastic sphere whose density is 1150 kg/m3 is dropped into water at 20°C. Determine the terminal velocity of the sphere in water. The density and dynamic viscosity of water at 20°C are rho = 998 kg/m3 and μ = 1.002×10-3 kg/m⋅s, respectively. The drag coefficient for a sphere in laminar flow is CD = 0.5.

Answer 1

Answer:

0.044 m/s

Explanation:

We are given that

Diameter of plastic sphere=11 mm=$11\times 10^{-3}=0.011 m$

Density of sphere=$1150 kg/m^3$

T=$20^{\circ} C$

Density of water=$998 kg/m^3$

Viscosity of water=$1.002\times 10^{-3} kg/ms$

Drag coefficient of a sphere in a laminar flow $C_D=0.5$

We have to find the terminal velocity of the sphere in water.

Terminal velocity of sphere in water is given by

$V=\sqrt{\frac{4gD(\frac{\rho_s}{\rho_w}-1)}{3C_D}$

Substitute the values then we get

$V=\sqrt{\frac{4\cdot 9.81\times 0.011(\frac{1150}{998}-1)}{3\times 0.5}$

$V=0.044 m/s$

Hence, the terminal velocity of sphere in water=0.044 m/s