Question

A copper sphere 10 mm in diameter is dropped into a 1-m-deep drum of asphalt. The asphalt has a density of 1150 kg/m3 and a viscosity of 105 N.s/m2 . Estimate the time it takes for the sphere to reach the bottom of the drum

Answer 1

Answer:

t = 1964636.542 sec

Explanation:

Given data:

sphere diameter is 10 mm

Density is 1150 kg/m^3

viscosity 105 N s/m^2

We knwo that time taken by sphere can be calculated by following procedure

$\tau = \mu \frac{du}{dy}$

$\frac{F}{A} = \mu \frac{du}{r}$

$\frac{\rho_C -\rho_{asphalt} gv}{2 \pi rL} = 10^5 \frac{du}{r}$

Solving for du

$du = \frac{ (8933 - 1150) 9.81 \frac{4}{3} \pi (10\times 10^{-3})^3}{2\pi \times 1\times 10^5}$

$du = u = 5.09\times 10^{-7}$

$u = \frac{1}{t}$

$t = \frac{1}{5.09\times 10^{-7}} = 1964636.542 sec$