Question

The largest and the smallest balls used in the experiment are with diameter 9.52 mm, and 2.38 mm respectively. For a glycerin with viscosity 1.5 Pa.s, what is the time necessary for each ball to rich a velocity 99% of the terminal velocity? Density of the ball material is given in the text. Round the result to three decimal places.

Answer 1

given,

largest diameter of balls = 9.52 mm = 0.00476 m

radius = 0.00476

smallest diameter of ball = 2.38 mm = 0.00238 m

radius = 0.00119

viscosity = 1.5 Pa.s

density of the ball = 1.42 g/cm

`F = 6\pi \eta r V_t`

`F = (mv)/(t)`

`F = ((4)/(3)\pi\ r^3* (\rho-\sigma) * 0.99 V_T)/(t)`

`6\pi \eta r V_t = ((4)/(3)\pi\ r^3* rho * 0.99 V_T)/(t)`

`t = ((4)/(3)\pi\ r^3* rho * 0.99 V_T)/(6\pi \eta r V_t)`

`t= (0.22 r^2 (\rho-\sigma) )/(\eta)`

for small balls

`t= (0.22* 0.00119^2 (1460-1300))/(1.5)`

t = 0.033 ms

for larger ball

`t= (0.22* 0.00476^2 (1460-1300))/(1.5)`

t = 0.531 ms