This is a demonstration of the concept of conservation of mass. By pouring an incompressible fluid (molasses), it is clearly demonstrated that as the velocity of the flow increases, the cross-sectional area of the flow must decrease. This demonstration should take 8-10 minutes.
Mass is conserved when the mass flow rate into the system equals the mass flow rate out of the system:
The mass flow of a fluid at any point is the product of the density, cross-sectional area and flow velocity. Therefore, we can rewrite the conservation of mass between points one and two as:
The density of molasses is assumed constant between points one and two and equation (2) reduces to:
If the cross-sectional area of the flow decreases (), then the flow velocity must increase to maintain the conservation of mass ().
What You Need
|Jar of Molasses||1||Any kind will do.|
|Beaker||1||Any kind of cup will suffice to collect the molasses|
|Wet Paper Towels||5-10||Used for the inevitable mess|
How It’s Done
Before Class: Open the jar of molasses as it will inevitably be stuck shut otherwise during class.
In Class: After a discussion of the conservation of mass, pour the molasses from the jar or a cup into the beaker. The cross-sectional area of the flow initially () is large and the flow velocity () is low. As the flow accelerates due to gravity, the downstream velocity () increases (figure below, bottom left). As this velocity increases we see the cross-sectional area () decrease (figure below, bottom right).
Observations: Students should be able to observe how the cross-sectional area decreases as the velocity increases.
Additional Application: Ask the students for common examples where we increase the flow velocity by decreasing the area (i.e. shower head, squirt gun, etc.). Using these examples, draw a schematic of the device illustrating the conditions at points one and two.