Loading in 5 sec....

Analysis of DisturbancePowerPoint Presentation

Analysis of Disturbance

- 75 Views
- Uploaded on

Download Presentation
## PowerPoint Slideshow about ' Analysis of Disturbance' - jaimin

**An Image/Link below is provided (as is) to download presentation**

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.

- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -

Presentation Transcript

### Analysis of Disturbance

P M V Subbarao

Associate Professor

Mechanical Engineering Department

I I T Delhi

Modeling of A Quasi-static Process in A Medium …..

Conservation Laws Applied to 1 D Steady disturbance

Conservation of Mass:

Conservation of Mass for 1DSF:

c-u

p, r ...

C

P+dp, r+dr ...

Change is final -initial

For infinitesimally small disturbance

Assume ideal gas conditions for Conservation of Momentum :

For steady flow momentum equation for CV:

For steady 1-D flow :

Nature of Substance

- The expressions for speed of sound can be used to prove that speed of sound is a property of a substance.
- Using the momentum analysis :

- If it is possible to obtain a relation between p and r, then c can be expressed as a state variable.
- This is called as equation of state, which depends on nature of substance.

Speed of sound in ideal and perfect gases

- The speed of sound can be obtained easily for the equation of state for an ideal gas because of a simple mathematical expression.
- The pressure for an ideal gas can be expressed as a simple function of density and a function molecular structure or ratio of specific heats, gnamely

Speed of Sound in A Real Gas

- The ideal gas model can be improved by introducing the compressibility factor.
- The compressibility factor represents the deviation from the ideal gas.
- Thus, a real gas equation can be expressed in many cases as

Isentropic Relation for A Real Gas

Gibbs Equation for a general change of state of a substance:

Isentropic change of state:

Pfaffian Analysis of Enthalpy

For a pure substance :

For a change of state:

Enthalpy will be a property of a substance iff

The definition of pressure specific heat for a pure substance is

Gibbs Function for constant pressure process :

Gibbs Function for constant temperature process : substance is

Divide all terms by dp at constant temperature:

Isentropic Relation for A Real Gas substance is

Speed of sound in real gas substance is

Speed of Sound in Almost Incompressible Liquid substance is

- Even flowing Liquid normally is assumed to be incompressible in reality has a small and important compressible aspect.
- The ratio of the change in the fractional volume to pressure or compression is referred to as the bulk modulus of the liquid.
- For example, the average bulk modulus for water is 2 X109N/m2.
- At a depth of about 4,000 meters, the pressure is about 4 X 107N/m2.
- The fractional volume change is only about 1.8% even under this pressure nevertheless it is a change.
- The compressibility of the substance is the reciprocal of the bulk modulus.
- The amount of compression of almost all liquids is seen to be very small.

Speed of Sound in Solids substance is

- The situation with solids is considerably more complicated, with different speeds in different directions, in different kinds of geometries, and differences between transverse and longitudinal waves.
- Nevertheless, the speed of sound in solids is larger than in liquids and definitely larger than in gases.
- Sound speed for solid is:

Speed of Sound in Two Phase Medium substance is

- The gas flow in many industrial situations contains other particles.
- In actuality, there could be more than one speed of sound for two phase flow.
- Indeed there is double chocking phenomenon in two phase flow.
- However, for homogeneous and under certain condition a single velocity can be considered.
- There can be several models that approached this problem.
- For simplicity, it assumed that two materials are homogeneously mixed.
- The flow is mostly gas with drops of the other phase (liquid or solid), about equal parts of gas and the liquid phase, and liquid with some bubbles.

Download Presentation

Connecting to Server..