# Drag Coefficient and Reynolds Number Related to free fall

• lucas
In summary, the speaker is conducting a theoretical investigation to determine the time it will take for an object, a 5x5x5 cm cube, to fall from a height of 30m. They have the Reynolds number and need to calculate the drag coefficient and terminal velocity. They are stuck and need an equation for the drag coefficient as a function of the Reynolds number. Chet suggests looking up drag over a sphere as it may be closer to what they need.
lucas

## 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.

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.

lucas said:
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

Hi there,

First of all, great job on your theoretical investigation! It's always good to compare your theoretical results with experimental data to validate your calculations.

To solve for the drag coefficient (Cd), we can use the formula you provided: Cd = Fdrag / (0.5 * ρ * Asurface * V^2 * Cdrag). Since we know the air density (ρ) and the area (Asurface), we just need to find the drag force (Fdrag) and the cube's velocity (V) to solve for Cd.

To find the drag force, we can use the formula Fdrag = 0.5 * ρ * V^2 * Cd * Asurface. We already know the air density and the area, so we just need to find the cube's velocity (V) at a height of 30m.

To do this, we can use the free fall equation: H = 1/2 * g * t^2, where H is the height, g is the acceleration due to gravity (9.8 m/s^2), and t is the time it takes the object to fall. We can solve for t by rearranging the equation to t = √(2H/g).

Plugging in our values (H = 30m and g = 9.8 m/s^2), we get t = √(2*30/9.8) = 2.73 seconds. This is the time it takes for the cube to reach a velocity of 12.15 m/s (which you calculated earlier).

Now, we can plug in our values for Fdrag and V into the drag force formula to solve for Cd: Cd = Fdrag / (0.5 * ρ * Asurface * V^2 * Cdrag). This will give us the drag coefficient for our cube.

To find the terminal velocity, we can use the formula Vterminal = √(2mg/ρAsurfaceCd), where m is the mass of the cube. Since we know the dimensions of the cube (5x5x5 cm), we can calculate its volume (V = 125 cm^3) and use the density of the cube (ρcube = 1.25 kg/m^3) to find its mass (m = ρcube * V = 1.25*10^-3 kg).

Plugging in our values, we get Vterminal =

## What is drag coefficient and how does it relate to free fall?

Drag coefficient is a dimensionless quantity that measures the resistance of an object moving through a fluid, such as air, and is denoted by the symbol Cd. It is a ratio of the drag force to the product of the fluid density, the reference area, and the square of the velocity. In free fall, the drag coefficient is an important factor in determining the terminal velocity of an object.

## What factors affect the drag coefficient?

The drag coefficient is affected by several factors, including the shape and size of the object, the fluid density, the viscosity of the fluid, and the velocity of the object. The surface roughness of the object and the presence of any obstacles in the fluid flow can also affect the drag coefficient.

## What is the Reynolds number and how is it related to free fall?

The Reynolds number is a dimensionless quantity that represents the ratio of inertial forces to viscous forces in a fluid flow. It is denoted by the symbol Re and is calculated using the object's velocity, size, and the properties of the fluid. In free fall, the Reynolds number is used to determine whether the flow around an object is laminar or turbulent, which can affect the drag coefficient and the object's terminal velocity.

## How do you calculate the drag coefficient and Reynolds number for an object in free fall?

The drag coefficient can be calculated using the formula Cd = Fd / (ρAv2/2), where Fd is the drag force, ρ is the fluid density, A is the reference area, and v is the velocity of the object. The Reynolds number can be calculated using the formula Re = ρvd/μ, where μ is the dynamic viscosity of the fluid and d is the characteristic length of the object. These calculations may vary depending on the specific situation and object in free fall.

## How does understanding drag coefficient and Reynolds number impact the design of objects for free fall?

Understanding the drag coefficient and Reynolds number is crucial in the design of objects for free fall, such as parachutes, skydiving equipment, and spacecraft. Designers need to consider these factors to minimize drag and achieve the desired terminal velocity. By optimizing the shape and size of the object, as well as the materials used, designers can improve the aerodynamic performance and safety of objects in free fall.

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