Dimensional analysis, I'm kinda lost

[coasterguy]

Homework Statement

* The force of wind acting on a body can be computed by the formula:

F = 0.00256 Cd V2 A

where:

F = wind force (lbf)

Cd= drag coefficient (no units)

V = wind velocity (mi/h)

A = projected area(ft2)

* To keep the equation dimensionally homogeneous, what are the units of 0.00256?

The Attempt at a Solution

I'm really new to this, and the professor didn't explain it well. IDK if I did that right so far, but I'm not sure what to do next. What does it mean by the units of .00256? Thanks

 

[djeitnstine]

Since you know this already, I will answer your question with another question.

What is the full definition of [tex]C_d[/tex] ?

What 2 important variables are missing to non-dimensionalize that term there?

As your topic implies, check your units.

 

[tomcue]

Dimensional analysis is a powerful tool used in science and engineering to ensure that equations are consistent and meaningful. In this case, the units of 0.00256 must be determined in order for the equation to be dimensionally homogeneous, meaning that all units on both sides of the equation must match.

To determine the units of 0.00256, we can use the given equation and the units of the other variables to solve for the units of 0.00256. Starting with the units on the right side of the equation, we have lbf = no units * (mi/h)^2 * ft^2. Simplifying this, we get lbf = ft^2 * mi^2/h^2. Now, we can compare this to the units on the left side of the equation, which is lbf. We can see that the units of 0.00256 must be ft^2 * mi^2/h^2 in order for the equation to be dimensionally homogeneous.

In summary, the units of 0.00256 are ft^2 * mi^2/h^2, which means that it is a conversion factor that allows us to convert the units of wind velocity (mi/h) and projected area (ft^2) into the units of wind force (lbf). I hope this helps clarify the concept of dimensional analysis for you. If you have any further questions, please don't hesitate to ask your professor or seek additional resources. Good luck with your studies!