How do I write the code for the following equation?

Raindrop acceleration equation:

dv(t)/dt = g - Cd * (Pa/Pw)* (3v(t)*2/4d)

Given that v(0) = 0

Answer 1

[Ameer Hamza]

If you have symbolic toolbox, you can find the symbolic solution

syms v(t)

g = 9.8;
Pa = 1;
Pw = 2;
d = 5;
Cd = 0.2;

eq = diff(v) == g - Cd*(Pa/Pw)*3*v(t)*2/(4*d);
IC = v(0) == 0;

sol = dsolve(eq, IC);
fplot(sol, [0 200])

Result

Otherwise, you can find the numerical solution using ode45()

g = 9.8;
Pa = 1;
Pw = 2;
d = 5;
Cd = 0.2;

dv = @(t,v) g - Cd*(Pa/Pw)*3*v*2/(4*d);
IC = 0;
tspan = [0 200];

[t, y] = ode45(dv, tspan, IC);
plot(t, y)

[Choi Ying WONG]

Thanks. However, I have to use the data above to complete the work. So do you mean that I just have to change the value of diameter to obtain the value?

The given density of water is 1000 kg/m^3. When I changed the value of Pw to 1000, the graph becomes a straight line instead of curve. How do I fix this?

[Ameer Hamza]

Yes, you just need to change the parameters. Can you give me the set of parameters which create straight line?

[Choi Ying WONG]

I use the small drop with diameter = 0.5mm as an example from the table (sent above).

[Ameer Hamza]

It is also curved. But the curve starts at large value of 't'. Increase the tspan

tspan = [0 5000];

[Choi Ying WONG]

It works now. Thanks so much.

[Ameer Hamza]

I am glad to be of help!