### Model Description

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. ### Engineering Principle

Mass is conserved when the mass flow rate into the system equals the mass flow rate out of the system: $\dot{m_{in}} = \dot{m_{out}}$

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: $\rho_1A_1V_1 = \rho_2A_2V_2$

The density of molasses is assumed constant between points one and two and equation (2) reduces to: $A_1V_1 = A_2V_2$

If the cross-sectional area of the flow decreases ( $A_2 < A_1$), then the flow velocity must increase to maintain the conservation of mass ( $V_2 > V_1$).

### What You Need

Item Quantity Description/Clarification
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 ( $A_1$) is large and the flow velocity ( $V_1$) is low.  As the flow accelerates due to gravity, the downstream velocity ( $V_2$) increases (figure below, bottom left). As this velocity increases we see the cross-sectional area ( $A_2$) 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.

### Cite this work as:

Phil Root (2019), "Molasses Madness," https://www.handsonmechanics.org/thermal/621.