FLUID DYNAMICS
FLUID DYNAMICS
Ms.Arockia Jayaseely,M.sc.,M.Phil.,
Assistant professor
Dept. of Maths, shift-II
1
Fluids and solids
•
Fluids is any substance that flows.
•
Solid is any substance that does not flows.
Fluid Dynamics
1.
Science treating the study of fluid in motion.
2.
it is a branch of
mechanics.
2
f
l
u
i
d
s
Fluids, they are two kinds
************************************
Liquids
-------->
Incompressible
Gas
-------
->
Compressible
3
Kinematics of fluids in motion
Real fluids and Ideal fluids
Orthogonal curvilinear system
Let P(x,y,z) be any point in space with respect to a triangular
co-ordinate system , suppose there exists uniform curves
•
λ
(x,y,z)=k
•
μ
( x,y,z)=m ---------1
•
ϒ(x,y,z)=n
4
Streamlines
1
5
2
6
It is based on the following assumptions:
•
The fluid is non-viscous (i,e., the frictional
losses are zero).
•
The fluid is homogeneous and
incompressible (i.e., mass density of the
fluid is constant).
•
The flow is continuous, steady and along
the streamline.
•
The velocity of the flow is uniform over
the section
7
Stream line
8
9
1.
Pathline
2.
Streamline
3.
Flux through a surface:
Only the normal component of the local relative velocity of
fluid with respect to the surface ( ) can transport fluid across
the surface.
Pathline & Streamline
10
Coincidence of Pathlines, Streamlines,
Streaklines
•
Unsteady flows:
Pathlines, streamlines, and streaklines are not the same.
•
Steady flows:
Pathlines, streamlines, and streaklines are identical.
THANK YOU
11
World of fluid dynamics, analyzing fluid motion, identifying types of fluids, studying streamlines, and understanding key assumptions. Delve into concepts like pathlines, streaklines, and the impact of steady vs. unsteady flows. Discover the fundamental principles in fluid dynamics presented in a clear and informative manner.
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Presentation Transcript
1 FLUID DYNAMICS Ms.Arockia Jayaseely,M.sc.,M.Phil., Assistant professor Dept. of Maths, shift-II
2 Fluids and solids Fluids is any substance that flows. Solid is any substance that does not flows. Fluid Dynamics Science treating the study of fluid in motion. it is a branch of mechanics. 1. 2.
3 fluids Fluids, they are two kinds Fluids, they are two kinds ************************************ Liquids --------> Incompressible Gas --------> Compressible
4 Kinematics of fluids in motion Real fluids and Ideal fluids Orthogonal curvilinear system Let P(x,y,z) be any point in space with respect to a triangular co-ordinate system , suppose there exists uniform curves (x,y,z)=k ( x,y,z)=m ---------1 (x,y,z)=n
5 Streamlines 1
6 2
7 It is based on the following assumptions: The fluid is non-viscous (i,e., the frictional losses are zero). The fluid is homogeneous and incompressible (i.e., mass density of the fluid is constant). The flow is continuous, steady and along the streamline. The velocity of the flow is uniform over the section
8 Stream line
9 Pathline & Streamline = dx udt v d x dx dy v dz 1. Pathline = ( t x , ) V = = = = , dy dt or dt dt u w = dz wdt dx dy v dz = ( ) // ( , ) d x V x t = = = d ( , ) d x k V x t Streamline 2. u w where is non a - vanishing scalar k 3. Flux through a surface: Only the normal component of the local relative velocity of fluid with respect to the surface ( ) can transport fluid across V/ f s n the surface.
10 Coincidence of Pathlines, Streamlines, Streaklines Unsteady flows: Pathlines, streamlines, and streaklines are not the same. Steady flows: Pathlines, streamlines, and streaklines are identical.
11 THANK YOU
