Mass Flow Rate

• The conservation of mass is a fundamental concept of physics. Within some problem domain, the amount of mass remains constant --mass is neither created nor destroyed. 
• The mass of any object is simply the volume that the object occupies times the density of the object. For a fluid (a liquid or a gas) the density, volume, and shape of the object can all change within the domain with time. And mass can move through the domain. 

• On the figure, we show a flow of gas through a constricted tube. There is no accumulation(Build up/growth) or destruction of mass through the tube; the same amount of mass leaves the tube as enters the tube. 
• At any plane perpendicular to the center line of the tube, the same amount of mass passes through. We call the amount of mass passing through a plane the mass flow rate. 
• The conservation of mass (continuity) tells us that the mass flow rate through a tube is a constant. We can determine the value of the mass flow rate from the flow conditions.

If the fluid initially passes through an area A at velocity V, we can define a volume of mass to be swept out in some amount of time t. The volume v is:

v = A * V * tA units check gives area x length/time x time = area x length = volume. The mass m contained in this volume is simply density r times the volume.

m = r * A * V * tTo determine the mass flow rate mdot, we divide the mass by the time. The resulting definition of mass flow rate is shown on the slide in red.

mdot = r * A * V