G Luhman, Mary ….
The acceleration of objects dropped from about 2 meters was found in order to derive the Reynolds Number. The effect of changing weight, shape, and radius of the objects (balloons) were tested independently such that it would be clear under what criteria either laminar or turbulent air flow is prevalent.
The difference between two models, laminar and turbulent, of air resistance may seem trivial the difference is can be seen everyday. Imagine the smoke rising from a small fire or a cigarette, at first the smoke will travel straight up in a linear manner (laminar flow) but then it begins to mix, swirl, and bellow, this is caused by the chaotic mixing and re-mixing of smoke with slightly different velocities and temperatures. For our experiment we look at how weight, size and shape of an object traveling through the air effects the acceleration of that object. Because the force of air resistance depends on whether laminar or turbulent flow is being experienced, we would expect to find accelerations that depended on not only weight but also on shape and size.
• Experimental Design
Our setup included a motion sensor pointed straight up, placed on the floor. An object was released at about two meters above the sensor such that the sensor recorded the position of the object as it fell. Objects were chosen such that they reached terminal velocity within our data set. This data was sent to DataStudio on the computer where the acceleration could be calculated. Once the acceleration was found, we can use Newton's 2nd Law (F=ma) and Terminal Velocity [F(gravity)=F(air resistance)] to determine the forces acting on the object. Our two models are defined with:
Laminar Flow (for a sphere):
F = 6 π η r v
where η is viscosity, r is the radius of the sphere, and v is the relative speed of the sphere
Turbulent Flow (for a sphere):
F = (1/2) π ρ Cd r2 v 2
where r and v are the same as above,...