# Drag Coeffecient and Reynolds Number. HELP

• freedomstatue

## Homework Statement

From dimensional analysis it is found that the drag force F that a fluid (density ρ, viscosity μ) exerts on a sphere (diameter d) moving through a fluid at a velocity u is given by

cD = f(Re),

where
.
The table below gives the relationship between the drag coefficient cD and the Reynolds number Re for spheres.

Re 10-1 100 101 102 103 104 105
cD 240 26.5 4.10 1.07 0.46 0.40 0.41

A spherical steel ball falling through a large expanse of oil attained a terminal velocity of 3.7 m s-1. What was the diameter of the steel ball?
Data: density of steel = 7800 kg m-3, density of oil = 920 kg m-3, viscosity of oil = 0.23 Pa s.

## Homework Equations

Obviously F=ma=ρV * a
Everything else is provided in the question except the sphere's diameter.

## The Attempt at a Solution

I had a method of equating both equations to "D" (diameter) since it is the variable which we wish to solve for. However, my lecturer told me I would only find the correct solution using one of the data point, which means this method is not efficient and won't get me any points. HELP please.

## Homework Statement

From dimensional analysis it is found that the drag force F that a fluid (density ρ, viscosity μ) exerts on a sphere (diameter d) moving through a fluid at a velocity u is given by

cD = f(Re),

where
.
The table below gives the relationship between the drag coefficient cD and the Reynolds number Re for spheres.

Re 10-1 100 101 102 103 104 105
cD 240 26.5 4.10 1.07 0.46 0.40 0.41

A spherical steel ball falling through a large expanse of oil attained a terminal velocity of 3.7 m s-1. What was the diameter of the steel ball?
Data: density of steel = 7800 kg m-3, density of oil = 920 kg m-3, viscosity of oil = 0.23 Pa s.

## Homework Equations

Obviously F=ma=ρV * a
Everything else is provided in the question except the sphere's diameter.

## The Attempt at a Solution

I had a method of equating both equations to "D" (diameter) since it is the variable which we wish to solve for. However, my lecturer told me I would only find the correct solution using one of the data point, which means this method is not efficient and won't get me any points. HELP please.

The sphere attaining a terminal velocity means that it is not accelerating, and a = 0. There are three forces acting on the sphere that are in equilibrium when the terminal velocity is attained. What are these three forces?