Question

Numerical method and Analytical method to calculate terminal velocity of a rain drop. (spherical shape and shape changing situations)

Answer 1

Analytical Method

Since air drag force is proportional for

taking drag force =

Let the mass of droplet be m

Applying the force balance balance equation on droplet

mg - = m dv/dt

at terminal velocity (steady state) -> dv/dt=0

=> v = (mg/b)^{0.5}

Numerical Method

Here the input of y₀ v₀ and no of steps 'n' is to be given. The steps are as below

1. Index: n

2. Time: t_n = t_n-1 + ∆t

3. The velocity at step n, v_n = v_n-1 + a_n-1∆t

4. The distance at step n: y_n = y_n-1 + v_n-1∆t

5. Net force at step n, F = mg- bv²

6. Net acceleration for next step, a_n= F_n/m