Prepared by: Abu UmeerChaman lal

Submitted to: Zulfiqar SolangiSubject: thermodynamics

Roll no:

14ch 42

14ch 39

Mehranuniversity

Faculty of science

Chemical department

4/20/2015 1

1. Conservation of mass and

energy principles in control

volume.

2.. Steady state and transient

form of mass and energy rate

balances.

contents

4/20/2015 2

4/20/2015 3

4/20/2015 4

4/20/2015 5

4/20/2015 6

4/20/2015 7

4/20/2015 8

4/20/2015 9

Forms of the mass and energy rate balance

The mass rate balance is a form that is

important for control volume analysis,

In many cases however, it is convenient to

apply the mass balance in forms suited to

particular objectives.

Some alternative form are as under,

1. One-dimensional flow form of the mass rate

balance .

2. Integral form of the mass rate balance

3.Stady state form of the mass rate balance

4/20/2015 10

STEADY STATE FORMS OF THE MASS

AND ENERGY RATE BALANCES

For a control volume at steady state, the

conditions of the mass within the control

volume and at the boundary do not vary

with time. The mass flow rates and the rates

of energy transfer by Heat and work are

also constant with time, there can be no

accumulation of mass within the

Control volume so,

dm/dt=o and the mass rate balance eq:

takes the form:

……… eq: 14/20/2015 11

Further more, at steady state de/dt=0 , so eq can be written as

… eq: 2

Alternatively,

………… eq: 3

Equation 1 asserts that at steady state the total rate at which mass enters the control volume Equals the total rate at which mass exits. Similarly, eq 3 asserts that the total rate at which Energy is transferred into the control volume equals the total rate at which energy is transferred out.

4/20/2015 12

many important application involve one-inlet,

one exit control volumes at steady State, it is

instructive to apply the mass and energy rate

balances to this special case.

The mass rate balance reduces simply to m1=m2

that is the mass flow rate must be the same At the

exit as it is at the inlet . The common mass flow

rate is designed simply by m . Next applyingThe energy rate balance and factoring the mass flow rate gives…

4/20/2015 13

or dividing by the mass flow rate.

…eq

5

The enthalpy, kinetic energy and

potential energy terms all appear in eq

5 as differences between their values

at the inlet and exit, this illustrates that

the datum used to assign values to

specific enthalpy, velocity and 4/20/2015 14

In eq: 5, the ratio q/m and wln are rates of

energy transfer per unit mass flowing

through

The control volume.

the foregoing steady-state forms of

the energy rate balance relate only energy

Transfer quantities evaluated at the

boundary of the control volume. no details

concerning

Properties within the control volume are

required by, or can be determined with,

these

Equation when applying the energy rate

balance in any of its forms, it is necessary to

Use the same units for all terms in the

4/20/2015 15