Question 1: Eight equal drops of oil are falling through air with steady velocity of 0.1 m/s. The drops recombine to form a single drop, what should be the new terminal velocity?
No of small drops = 8
Velocity of each individual drop = 0.1 m/s
No of large (combined) drops = 1
Terminal velocity of the combined drop
(1) Terminal velocity =
(2) Volume of the sphere,
|Mass of the small drop = m|
Volume of the small drop = V
Radius of the small drop = r
|Mass of the combined drop = M|
Volume of the combined drop = Vc
Radius of the combined drop = R
Terminal velocity of the combined drop = VcT
For the solution, we need to find the radius R of the combined drop and then put it in the formula 1 to find the terminal velocity of the combined drop. For the calculation of R, we use formula 2.
Take cube root of the eqution
Put this value in Formula (1) for the terminal velocity of the combined larger drop.
But M = 8m, therefore,
On the RHS, the value in bracket is the terminal velocity of the small droplets. So put it,
Where v = 0.1 m/s is the velocity of the small drop given in the text.
Since the density of the individual droplets and the big drop is same, we also can apply the equation . Use this equation to solv the problem.