General Conservation of Energy and mass principles for control volume

S.Gunabalan Associate Professor Mechanical Engineering Department Bharathiyar College of Engineering & Technology Karaikal - 609 609. e-Mail : gunabalans@yahoo.com

Part - 1

TERMODYNAMIC ANALYSIS OF CONTROL VOLUMES

A large number of engineering problems involve mass flow in and out of a system and, therefore, are modeled as CONTROL VOLUMES.

TERMODYNAMIC ANALYSIS OF CONTROL VOLUMES

A water heater, a car radiator, a turbine, and a compressor all involve mass flow and should be analyzed as control volumes (OPEN SYSTEMS) instead of as control mass (CLOSED SYSTEMS). In general, any arbitrary region in space can be selected as a control volume. The boundaries of a control volume are called a CONTROL SURFACE and they can be real or imaginary.

TRANSIENT

STEADY implies “NO CHANGE WITH TIME”. The opposite of steady is UNSTEADY, or TRANSIENT.

General Conservation mass principles for control volume

The conservation of mass is one of the most fundamental principles in nature. For closed systems, the conservation of mass principle in implicitly used by requiring that the mass of the system remain constant during a process. For control volumes, however, mass can cross the boundaries, and so we want must keep track of the amount of the mass entering and leaving the control volume. The CONSERVATION OF MASS PRINCIPLE for a control volume (CV) undergoing a process can be expressed as

General Conservation mass principles for control volume

General Conservation mass principles for control volume

General Conservation mass principles for control volume

• MASS AND VOLUME FLOW RATES – The amount of mass flowing through a cross – section per unit time is called the MASS FLOW – RATES Denoted as “w” – A liquid or gas flows in and out of a control volume

through pipes or ducts. The mass flow rate of a fluid flowing in a pipe or duct is proportional to the cross-sectional area A of the pipe or duct, the density , ρ and the velocity ν of the fluid. The mass flow rate through a differential area dA can be expressed as Where ν the velocity component normal to dA. The mass flow rate through the entire cross sectional area of the pipe or duct is obtained by integration

General Conservation mass principles for control volume

• Conservation of mass – The mass flow rate of a system at entry equal to

mass flow rate at exit of the system 푤푖푛푙푒푡 = 푤표푢푡푙푒푡

푤 = 퐴1푽1

푣1= 퐴2푽2

푣2

This is Equation of Continuity 푽 – Velocity of flow

General Conservation mass principles for control volume

• The volume of the fluid flowing through a cross-section per unit time is called the VOLUME FLOW RATE = 퐴1푽1 m3/s

General Conservation of Energy for control volume

풆풙풑풓풆풔풔풆풅풂풔풕풓풂풏풔풇풆풓풂풄풓풐풔풔풕풉풆풔풚풔풕풆풎풃풐풖풏풅풂풓풚. 푻풉풊풔풘풂풔풅풖풓풊풏품풂풑풓풐풄풆풔풔풊풔풆풒풖풂풍풕풐풕풉풆풏풆풕풉풆풂풕풂풏풅 풘풐풓풌푻풉풆풄풉풂풏품풆풊풏풕풉풆풆풏풆풓품풚풐풇풂풄풍풐풔풆풅풔풚풔풕풆풎 푄 −푊 = ∆퐸

For control volumes, however, an additional mechanism can change the energy of a system: MASS FLOW IN AND OUT OF THE CONTROL VOLUME.

General Conservation of Energy for control volume

When mass enters a control volume, the energy of the control volume increases because the entering mass carries some energy with it. Likewise, when some mass leaves the control volume, the energy contained within the control volume decreases because the leaving mass takes out some energy with it.

The conservation of energy equation for a control volume undergoing a process can be expressed as

The energy required to push fluid into or out of a control volume is called the FLOW WORK, or FLOW ENERGY TOTAL ENERGY OF A FLOWING FLUID

General Conservation of Energy for control volume

풘(ℎ1 + 푉1 2 + 푔푧1) + 푄

= 풘(ℎ2 + 푉2 2 + 푔푧2) + 푊

Energy Balances on Open Systems also called Conservation of Energy for control volume

Ref: http://www.me.uprm.edu/o_meza/INME4045/4tochapter-INME4045.pdf

Define steady-flow process and its Characteristics

A steady-flow process can be defined as A PROCESS DURING WHICH A FLUID FLOWS THROUGH A CONTROL VOLUME STEADLY. That is, the fluid properties can change from point it point within the control volume, but at any fixed point they remain the same during the entire process. (STEADY means NO CHANGE WITH TIME.)

A steady-flow process is characterized by the following

1. No properties (intensive or extensive) within the control volume change with time. 2. No properties change at the boundaries of the control volume with time. 3. The heat and work interactions between a steady-flow system and its surrounding do not change with time.

• During a steady-flow process fluid properties within the control volume may change with position, but no with time • Under steady-flow conditions, the mass and

energy contents of a control volume remain constant.

Reference • http://www.me.uprm.edu/o_meza/INME4045/4tochapter-INME4045.pdf