 Ch 3. First Law of Thermodynamics Multimedia Engineering Thermodynamics Conservationof Mass Conservationof Energy Solids andLiquids Ideal Gas
 Chapter 1. Basics 2. Pure Substances 3. First Law 4. Energy Analysis 5. Second Law 6. Entropy 7. Exergy Analysis 8. Gas Power Cyc 9. Brayton Cycle 10. Rankine Cycle Appendix Basic Math Units Thermo Tables Search eBooks Dynamics Statics Mechanics Fluids Thermodynamics Math Author(s): Meirong Huang Kurt Gramoll ©Kurt Gramoll THERMODYNAMICS - THEORY

Mass and Volume Flow Rate Mass Flow Rate Through a Duct

The mass flow rate ( ) is defined as the amount of mass flowing through a cross-section per unit time. The mass flow rate of a fluid flowing in or out of a pipe or duct is proportional to the cross-sectional area (A) of the pipe or duct, the density of the fluid (ρ), and the velocity of the flow (V). The flow rate through a differential area dA is:

d = ρVndA

where
Vn = the velocity component normal to the area dA Normal Velocity Component

Integrating the above equation to get the total mass flow rate. The volume flow rate ( ) is the volume of the fluid flowing through a cross-sectional area per unit time. The mass and volume flow rate are related by Conservation of Mass Principle System Used for
Conservation of Mass Equation

The conservation of mass principle states the following:

 Net mass transfer to or from a system during a process is equal to the net change in the total mass of the system during that process.

In an equation format, the conservation of mass principle is:

(Total mass entering the system)
-
(Total mass leaving the system)
=
(Net change in mass within the system) Filling and Emptying Bathtub is an
Example of Mass Conservation

or,

min - mout = Δmsystem

where
Δmsystem = msystem@final - msystem@initial

The rate form of the conservation of mass principle is:

(Rate at which mass entering the system)
-
(Rate at which mass leaving the system)
=
(time rate of change in mass within the system)

or, Conservation of Mass for Closed System Mass Remains Constant for a
Closed System

A closed system is defined as a system which mass can not cross its boundaries, but energy transfer is allowed. Since no mass flows in or out of the system, the mass of the closed system remains constant during a process. 