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

To estimate the time it takes for the copper sphere to reach the bottom of the drum, you can use the concept of terminal velocity and Stoke's Law. First, calculate the terminal velocity using the drag force. Then, use the equation 'time = distance / velocity' to estimate the time taken.

Step-by-step explanation:

The time it takes for the copper sphere to reach the bottom of the drum can be estimated using the concept of terminal velocity. Terminal velocity is the constant speed that an object reaches when the drag force acting on it is equal to the gravitational force pulling it down.

First, we need to calculate the terminal velocity of the copper sphere. The drag force acting on the sphere can be calculated using Stoke's Law: FD = 6πηrv, where η is the viscosity of the fluid, r is the radius of the sphere, and v is the velocity of the sphere.

Once we have the terminal velocity, we can use the equation time = distance / velocity to estimate the time it takes for the sphere to reach the bottom of the drum.

Answer 2

t = 1964636.542 sec

Step-by-step 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 (du)/(dy)`

`(F)/(A) =  \mu (du)/(r)`

`(\rho_C -\rho_(asphalt) gv)/(2 \pi rL) = 10^5 (du)/(r)`

Solving for du

`du = ( (8933 - 1150) 9.81 (4)/(3) \pi (10* 10^(-3))^3)/(2\pi * 1* 10^5)`

`du = u = 5.09* 10^(-7)`

`u = (1)/(t)`

`t = (1)/(5.09* 10^(-7)) = 1964636.542 sec`