# Relating the Reynolds number to the Drag Coeffient

• Noone1982
In summary, the conversation discusses the relationship between the Reynolds number and the drag coefficient. It is mentioned that the drag coefficient must be determined experimentally for different velocities, while the Reynolds number can be used to determine laminar or turbulent flow. The equation for calculating the drag coefficient is given, as well as the equation for Reynolds number. There is some confusion about how to solve for the drag coefficient in terms of the Reynolds number, and whether the viscosity of the medium affects the calculation.
Noone1982
How does one relate the Reynolds number to the Drag Coeffient?

It seems the drag coefficient for different velocities must be determined experimentally per set. I know the Reynolds number is a method to determine laminar or turbulent flow, but can it be used to determine the drag coefficient?

See discussion on drag coeffient and the relationship between drag force and velocity here.
http://www.grc.nasa.gov/WWW/K-12/airplane/dragco.html

In addition, Reynolds number is a function of velocity, and density, characteristic dimension (length), and viscosity.

One can relate Re and Cd through velocity.

The Drag coefficient is given by,

$$\mbox{C}d\; =\; \frac{1}{2}\mbox{C}d\left( v \right)Apv^{2}$$

And the Reynolds number is given by,

$$\mbox{Re}\; =\; \frac{vpl}{\mu }$$

I'm failing to see how to solve Cd in terms of the Reynolds number since the Reynolds number doesn't contain a drag force.

Anyone? The clock is ticking :(

Taking $$Re\, =\, \frac{\rho vl}{\mu }$$, then

$$Re^2\, =\, \frac{(\rho vl)^2}{\mu^2 }$$, or

$$Re^2(\frac{\mu}{l})^2\, =\,(\rho v)^2}$$

The one looks at Cd

$$C_d\; =\; \frac{1}{2}C_d\left( v \right)A\frac{(\rho v)^{2}}{\rho}$$

then do appropriate substitution.

Does it matter if the medium has a very high viscosity? We were looking at a calculation in sea water with a Poise of 1.025. Some gents said that the calculation that we used should use v2 instead of v. What do the gurus think?

Unless you have some special kind of Cd, the drag force is usually proportional to v^2 rather than v. Without knowing what specific calculation you are talking about, deponent further sayeth not.

## What is the Reynolds number?

The Reynolds number is a dimensionless value used in fluid dynamics to determine the relative importance of inertial forces to viscous forces. It is calculated by multiplying the fluid velocity, fluid density, and characteristic length of the object, and dividing that by the fluid viscosity.

## How is the Reynolds number related to the drag coefficient?

The Reynolds number is directly related to the drag coefficient, which is a measure of the amount of drag force experienced by an object in a fluid flow. As the Reynolds number increases, the drag coefficient also increases, indicating a stronger influence of inertial forces and a higher drag force.

## What does a high Reynolds number indicate?

A high Reynolds number indicates a turbulent flow regime, meaning that the fluid is experiencing high levels of mixing and energy dissipation. This is typically seen at higher velocities or with larger objects.

## Why is it important to relate the Reynolds number to the drag coefficient?

Relating the Reynolds number to the drag coefficient allows scientists to understand and predict the behavior of objects in fluid flows. It helps to determine the amount of drag force an object will experience, which is crucial in many engineering applications such as aerodynamics and hydrodynamics.

## How can the Reynolds number be used in practical applications?

The Reynolds number is used in various industries, such as aerospace, automotive, and marine, to optimize the design of objects moving through fluids. It is also used in the analysis of fluid flow in pipelines and channels, and in the development of new technologies, such as wind turbines and submarines.

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