# Drag force to Velocity

1. Jul 9, 2009

### reality1980

Hi, I'm looking for the formula to get the velocity value from a drag value. I found plenty of resources to do it the other way around (velocity to drag) but no luck to get it the way I need it.

This website seems to have it but they don't provide the rule and they actually want money to enable the calculate button... http://www.lmnoeng.com/Force/DragForce.htm

So basically I have the drag force value, the fluid density, area, force and drag coeff., I want to get the velocity from that.

For some context, I want to use a force sensing cell with a known area facing water towards the heading direction and get my speed value from the force exerted by the water on the sensing cell.

Could anybody help me geopardize the equation to get it right?

2. Jul 9, 2009

### rock.freak667

If I remember fluid mechanics properly

then

$$F_{drag}= \frac{1}{2} \rho v^2 AC_d$$

3. Jul 9, 2009

### HallsofIvy

"Drag" is a force which is proportional to acceleration, not velocity. Do you mean the "terminal speed" when drag opposes some outside force?

(rock.freak667 gives a formula for drag as a function of speed.)

4. Jul 10, 2009

### reality1980

Ok yes, maybe I poorly explained what I wanted. Drag is proportional to acceleration, and it's not quite what I want. I'm not sure of the term to use here as I started searching for frontal resistance and wikipedia pushed me towards the drag term.

Let's use an example here... If you're on the road going 20MPH and stick your hand out the window, your hand will be pushed by the air rushing in (which I believe is named frontal resistance). This effect is proportional to speed, not to acceleration and will be constant at a given speed (no, there is no wind in this perfect theory world!). The faster you go, the more pressure is exerted on your hand.

I have a very similar setup; a load cell plate installed on the front of an aquatic vehicle measures the force at which the water pushes on it. I can get a force value with this measurement. Now I need to get a speed value from the force value, the area of the sensing plate and the fluid (water) density.

I'm aware that density changes with temperature but I can compensate for that. All I need is the basic formula to get my velocity.

Thanks :)

5. Jul 11, 2009

### HallsofIvy

That's a different matter. That's not a matter of the speed being a function of drag, it a matter of drag being a function of speed! If you have such a function then there must be one value of the drag for each speed but not necessarily a value of speed for each value of the drag, which is what you are asking for.