Eulerian method in fluid mechanics

Eulerian method in fluid mechanics
In the Eulerian description of fluid flow, individual fluid particles are not identified. Instead, a control volume is defined, as shown in the diagram. Pressure, velocity, acceleration, and all other flow properties are described as fields within the control volume. In other words, each property is expressed as a function of space and time, as shown for the velocity field in the diagram. In the Eulerian description of fluid flow, one is not concerned about the location or velocity of any particular particle, but rather about the velocity, acceleration, etc. of whatever particle happens to be at a particular location of interest at a particular time. Since fluid flow is a continuum phenomenon, at least down to the molecular level, the Eulerian description is usually preferred in fluid mechanics. Note, however, that the physical laws such as Newton's laws and the laws of conservation of mass and energy apply directly to particles in a Lagrangian description. Hence, some translation or reformulation of these laws is required for use with an Eulerian description.
Example - Pressure field - An example of a fluid flow variable expressed in Eulerian terms is the pressure. Rather than following the pressure of an individual particle, a pressure field is introduced, i.e.
p = p(x,y,z,t).
Note that pressure is a scalar, and is written as a function of space and time (x,y,z, and t). In other words, at a given point in space (x,y, and z), and at some particular time (t), the pressure is defined. In the Eulerian description, it is of no concern which fluid particle is at that location at that time. In fact, whatever fluid particle happens to be at that location at time t experiences the pressure defined above.
Example - Velocity field - An example of a fluid flow variable expressed in Eulerian terms is the velocity. Rather than following the velocity of an individual particle, a velocity field is introduced, i.e.
Note that since velocity is a vector, it can be split into three components (u,v, and w), all three of which are functions of space and time (x,y,z, and t). In other words, at a given point in space (x,y, and z), and at some particular time (t), the velocity vector is defined. In the Eulerian description, it is of no concern which fluid particle is at that location at that time. In fact, whatever fluid particle happens to be at that location at time t has the velocity defined above.
Example - Acceleration field - An example of a fluid flow variable expressed in Eulerian terms is the acceleration. Rather than following the acceleration of an individual particle, an acceleration field is introduced, i.e.
.Note that since acceleration is a vector, it can be split into three components, all three of which are functions of space and time (x,y,z, and t). In other words, at a given point in space (x,y, and z), and at some particular time (t), the acceleration vector is defined. In the Eulerian description, it is of no concern which fluid particle is at that location at that time. In fact, whatever fluid particle happens to be at that location at time t has the acceleration defined above.
Either description method is valid in fluid mechanics, but the Eulerian description is usually preferred because there are simply too many particles to keep track of in a Lagrangian description.
The Material Derivative, also called the Total Derivative or Substantial Derivative is useful as a bridge between Lagrangian and Eulerian descriptions.
Definition of the material derivative - The material derivative of some quantity is simply defined as the rate of change of that quantity following a fluid particle. It is derived for some arbitrary fluid property Q as follows:
KNOW MORE ABOUT Eulerian method in fluid mechanics AT;
www.mne.psu.edu...
en.wikipedia.o...
www.chegg.com/...
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[@kaursingh637]

sir -excellent --please suggest a book on hydro dynamics= thank u sir

[@captainasif226]

My prof. Asked me that where we put the Observer regarding this theory. So, could you Please let me know that what was he asking to me?

[@bishalkumargupta5649]

How mam last step..... az component (dw/dt) hoga kya.... Apna( dv/dt) likha ha

[@bishalkumargupta5649]

Mam aap do(2) or video banaiya
Topic -1)Relationship between Langrangian and eulerian method :-
a) Langrangian to Eulerian
b) Eulerian to Langrangian

[@eTution]

SORRY ALL IN ONE CHANNEL I AM NOT AT ALL GETTING WHAT U ARE SAYING CAN U PLEASE EXPLAIN IN BREF

[@learningvideos3946]

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[@MohanAbhishek]

While caliculating az= last the equation is wrong.

[@captainasif226]

Please let me know