Two rain drops each of radius r are falling with terminal velocity vt while in motion they coalesce into one drop what is the terminal velocity of the drop so formed?
1 Answer
Jun 14, 2018
Explanation:
For Rayleigh Drag:
-
#F_D = - 1/2 rho v^2A C_d# -
#rho# is fluid density,#A# is cross sectional area of object orthogonal to motion, and#C_d# is a constant
A falling object will accelerate as:
# F =ma=mg-1/2 rho v^2A C_d#
At terminal velocity,
Taking out the non-constants:
# v_t propto sqrt ( m / A) qquad square#
If two drops coalesce to form a new sphere, conservation of mass:
#m' = 2m#
For new radius
-
# 4/3 pi (r')^3 = 2 * 4/3 pi r^3 # -
# implies bb( r^' = 2^(1/3) r )# -
#A' = pi (r^')^2 = 2^(2/3) A # -
#(m')/(A') = 2^(1/3) m/A#
From