FLUID KINEMATICS

1. Chapter 5:Fluid Kinematics
Prepared by:
Er.Binu Karki
M. sc. iWRM
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2. Fluid Kinematics
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3. How do you define fluid flow?
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4. 4

5. 5

6. Lagrangian method
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• In this method, a single fluid particle is chosen and followed during its
motion.
• Its velocity, acceleration, density etc. is described with respect to its
location in space and time from a fixed position at the start of the
motion.
• The position of the fluid particle (x,y,z) at any time t with respect to
its position (a,b,c) at time t=0 is given as,
x=f1(a,b,c,t); y=f2(a,b,c,t); z=f3(a,b,c,t)
Then, velocity is given by
u=dx/dt ;v=dy/dt; w=dz/dt
ax =du/dt =d2x/dt2 ;ay= d2y/dt2 ; az= d2z/dt2
Resultant velocity=?
Resultant acceleration=?

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10. Eulerian method
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• In this method, a point or section is chosen in the flow field
• Its velocity, acceleration, density etc. are observed at that point
• It is a commonly used method because of mathematical simplicity
• Let u, v, and w be the components of resultant velocity in x, y and z
axis respectively. The velocity components vary along space and time.
u=f1(x,y,z,t);v=f2(x,y,z,t);w=f3(x,y,z,t)
Then, resultant velocity is given by
Resultant velocity=?

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12. Steady and Unsteady flow
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15. Steady and Unsteady flow
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19. Laminar and turbulent flow

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24. Laminar and turbulent flow
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29. Rotational and irrotational flow
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30. Rotational and irrotational flow
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• Rotational Flows :-
In which the fluid particles while flowing
along stream lines, rotate about their
own axis.
• Irrotational Flows:-
In which the fluid particles while flowing
along stream lines, do not rotate about their own
axis.
To test whether a flow has a rotational component,
you can put a small object in the flow and let the
flow carry it. If the small object spins, the flow is
rotational else the flow is irrotational

31. One , Two & Three
Dimensional Flows
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32. One , Two & Three
Dimensional Flows
• One Dimensional Flow:-
In which the flow parameter
such as velocity is a function of
time and one space co-ordinate only
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33. • Two Dimensional Flows:-
In which the velocity is a function of time
and two rectangular space co-ordinates.
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34. Three Dimensional Flows:-
• In which the velocity is the function of time
and three mutually perpendicular
directions.
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35. Description of flow pattern
 Types of flow lines:
1. Path lines
2. Streamlines
3. Streak lines
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36. Pathline
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37. Streamlines
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• A streamline is a imaginary line drawn in
a flow field such that tangent drawn at
any point on it indicates the direction of
the velocity vector at that point.

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39. Streakline
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44. Equation of continuity
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49. Continued…
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50. Continued…
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51. Continuity equation in
Cylindrical Polar Co-ordinates
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52. Video!!
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55. Continued…
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56. Continued…
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57. Continued…
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58. Flow through stream tube
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59. Continued…
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60. Continued…
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