Work of Drag Force: Find k & n Values

[kbuild]

Homework Statement

Find work of drag force in term of proportional to Velocity
(Like: Wd=kV^n ,when k=constant value n=Real number)

Homework Equations

(Fd=1/2*ρ*v^2*Cd*A)

The Attempt at a Solution

I've a problem with my science project.
I try to find the terminal velocity of a group of tiny aquatic animal.
To find that I use Energy conserve, and to make it more realistic i should put drag force in my calculation.
So, i need to use drag force in term of work (Joule) to be able to mix with energy.

here is my attemption, Fd=1/2*ρ*v^2*Cd*A
Fd*s=1/2*ρ*v^2*Cd*A*s
Wd = k*V^2*s
umm, let me introduce you to my way to find the terminal velocity of a group of tiny aquatic animal in order to know my problem.
Given the group is in rectangle shape
Then i try to separate it into many layers to understand the effect of each part thoroughly.
so, i think there is no space between each layer... i don't know s

is there any fault in my logic? and how to solve this?

Thank you for your help :D

 

[Simon Bridge]

You want to know how the drag force depends on speed.
You are assuming it is quadratic with speed - is this a good assumption?
(Perhaps it is only an example?)

Since this is a "project", perhaps you need to do an experiment ... or is it not that kind of project?

It is not clear why you feel it will help to consider a "block" of "fish" instead of just doing the calc for one of them.

Anyway - looks like s is the distance the force acts over - which would be Vt.
If you divide through by time, you get power.

Note -
the rate you lose energy due to drag is (dW/dt)
so the fish needs to supply energy at this rate to maintain a constant kinetic energy and thus speed.

The speed the "fish" moves depends on the rate it supplies energy. If you know how drag varies with speed for the animal, and you observe it's speed, you can work out how efficiently it converts food into motive power - for example.

But it is usually easier to start from the balance of forces.

 

[kbuild]

Drag force is quadratic with speed according to Fd=1/2*ρ*v^2*Cd*A (is'nt it the normal equation?)

For my project, the tiny aquatic animal used in my project is 'euglena' which 80μm long.
So their group is about 1,000 units/mm^2.
In my opinion, it will complicate if i calculate every one of them.
And in my project, i'll find how to use their 'group' to push things with most efficiency.
i decided to use mathamatical model before do the experiment.

Group was separated to find the most effiiciency shape of euglena group or shape that can produce highest velocity(same group's mass).

I choosed 'work' and 'energy' because it's easy to measure(just measure velocity and mass).

I'll try to solve it on my matlab, thank you so much for your advice! ^_^
if some of my logic seem weird, please tell me.