Density

• Density is a scalar quantity; it has a magnitude but no direction associated with it. 
• An important property of any fluid is its density. Density is defined as the mass of an object divided by its volume, and most of our experiences with density involve solids.
• We know that some objects are heavier than other objects, even though they are the same size. A brick and a loaf of bread are about the same size, but a brick is heavier--it is more dense. 
• Among metals, aluminum is less dense than iron. That's why airplanes and rockets and some automobile parts are made from aluminum. For the same volume of material, one metal weighs less than another if it has a lower density.
• Since density is defined to be the mass divided by the volume, density depends directly on the size of the container in which a fixed mass of gas is confined. 

•  As a simple example, consider Case #1 on our figure. We have 26 molecules of a mythical gas. Each molecule has a mass of 20 grams (.02 kilograms), so the mass of this gas is .52 kg. We have confined this gas in a rectangular tube that is 1 meter on each side and 2 meters high. We are viewing the tube from the front, so the dimension into the slide is 1 meter for all the cases considered. The volume of the tube is 2 cubic meters, so the density is .26 kg/cubic meter. 
• This corresponds to air density at about 13 kilometers altitude. If the size of our container were decreased to 1 meter on all sides, as in Case #3, and we kept the same number of molecules, that density would increase to .52 kg/cubic meter. Notice that we have the same amount of material; it is just contained in a smaller volume. How we decrease the volume is very important for the final value of pressure and temperature. (This example REALLY works only for a very large number of molecules moving at random. Case #2 is just an illustration.) 
• Another way to obtain the same density for a smaller volume is to remove molecules from the container. In Case #4, the container is the same size as in Case #3, but the number of molecules (the mass) has been decreased to only 13 molecules. The density is .26 kg/cubic meter, which is the same density seen in the blue box of Case #2 and throughout Case #1. A careful study of these four cases will help you understand the meaning of gas density.

Note: For Density Problems, use the formula D=M/V
 For problems 1-4, use the mass and volume given to find the density of the column of air.

(1) Mass = 10 kg & Volume = 8m³

Density =_________

(2) Mass = 15 kg & Volume = 10m³

Density = _________

(3) Mass = 5 kg & Volume = 2m x 2m x 2m (Hint: You first need to calculate the volume!)

Density = _________

(4) Mass = 35 kg & Volume = 3m x 3m x 3m

Density = _________

Now answer the following questions.

(5) Looking at your answers above, which density will produce the greatest amount of lift(Raise)?

 

(6) Which will produce the least amount of lift?

 

(7) Given your answers to Problems 5 & 6 above, briefly state what effect the density of the air has on the lift of an airplane.