# Drag Coefficient and Reynolds Number Related to free fall

## Homework Statement

Hi, I am doing a theoretical investigation which will be compared to an experimental I'll do later. I am trying to calculate how much time will it take an object to fall a heigh H. the object is a 5x5x5 cm cube. I have the Reynolds number as this Re=3546*Velocity; and I need both the drag coefficient and the terminal velocity.

Air density ($\rho$): 1.25 kg/m3
Air Dynamic Viscosity ($\mu$): 1.76E-05
Area: 25 cm3
Cube side length: 0.05 m or 5 cm
Height (H): 30m

## Homework Equations

Re=$\frac{\rho*V*L}{\mu}$

Cd= Fdrag/0.5*ρ*Asurface*V2*Cdrag

## The Attempt at a Solution

Re=3546*V
I used classic mechanics to estimate the avarage of V for a height H of 30m, and got a value of 12.15 m/s so Re=3546*12.15.
I'm stuck from here on.
I need the Drag Coefficient, and the terminal V, and at what time does the object reach the velocity.

Chestermiller
Mentor
You need an equation for the drag coefficient as a function of the Reynolds number. Then you solve by trial and error to determine the velocity for which the drag force is equal to the weight of the cube.

Chet

Thank you Chet, but it is that equation that I can't seem to find, as there are a variety of equations; but no specification for which parameters.
For example: Cd=$\frac{0.664}{\sqrt{Re}}$ or Cd=$\frac{1.33}{\sqrt{Re}}$; and even Cd=0.0742 / Re1/5.

Chestermiller
Mentor
Thank you Chet, but it is that equation that I can't seem to find, as there are a variety of equations; but no specification for which parameters.
For example: Cd=$\frac{0.664}{\sqrt{Re}}$ or Cd=$\frac{1.33}{\sqrt{Re}}$; and even Cd=0.0742 / Re1/5.
The equations you have are for drag over a flat plate or for pressure drop in a tube. Look up drag over a sphere. This will get you closer to what you want. I don't think you will be able to find an equation for the drag coefficient for a cube, especially since it will vary with angle of attack.

Chet