Fluid mechanics Internal & External Flow.ppt

1. DEPARTMENT OF MECHANICAL ENGINEERING
Unit No. 5
Internal & External Flow
By
Prof. S. J. Suryawanshi

2. Internal Flow
Losses in Pipes

4. Numericals on Major loss:

9. Numericals on Minor loss:

12. Fig. showing Hydraulic grade line and energy line

13. Hydraulic Grade line and Total Energy line
As shown in the Figure above, whenever water flows from
tank 1 to tank 2, the energy equations for sections 1 , 2
and 3 with losses are as following:
where, h2 and h3 are the losses of head between
section 1 and either of the respective sections.

14. Syphon & Pipes in Series & Pipes in Parallel
Fig. Syphon

15. Numericals on Syphon –

18. Pipes in Series & Pipes in Parallel
• For Pipes in Series,
Discharge (Q) is same while Head (H) is different
• For Pipes in Parallel,
Head (H) is same while Discharge (Q) is different

19. Pipes in Series

21. Numericals on Pipes in Series –

24. Pipes in Parallel
• We Know, For Pipes in Parallel,

25. Numerical on Pipes in Parallel

28. External Flow
Boundary Layer Theory
• It is a thin layer close to the surface of a pipe.
• Near the boundary (stationary), velocity of fluid will be zero.
• Away from boundary in Y- direction, velocity of fluid goes on
increasing upto free stream velocity (Max velocity).
• This variation in velocity from zero to maximum velocity takes
place in a narrow region in a vicinity of a solid boundary which is
known as boundary layer.

29. As we know from the Newton’s law of Viscosity, the
velocity gradient across the fluid causes shear stress
formation which is nothing but the drag force.
• Now let’s us understand the terms involved in this
boundary layer i.e. what is
1. Boundary Layer thickness
2. Displacement Thickness
3. Momentum thickness
4. Energy thickness

30. Boundary Layer thickness
• It is defined as a distance from boundary of a solid body measured
in y- direction to the point, where the velocity of fluid is
approximately equal to 0.99 times free stream velocity (Max
Velocity) of flow.
• The velocity profile is parabolic in nature as you can see from the
figure. Generally the velocity profiles have equations of this form:

31. Boundary Layer Regions
1) Laminar boundary layer (AB)
2) Transition Boundary Layer (BC)
3) Turbulent Boundary Layer (CD)
4) Laminar Sub Layer

32. • Due to formation of boundary layer there is a
reduction in mass flow rate, momentum &
kinetic energy of a flowing fluid.
• Depending on this, boundary Layer thickness
can be measured in terms of
1. Displacement Thickness (Redution in mass)
2. Momentum thickness (Redution in momentum)
3. Energy thickness (Reduction in Energy)

33. 1. Displacement Thickness (δ*) :
It is defined as a distance measured perpendicular to the boundary of a
solid body, by which boundary should be displaced to compensate for
reduction in flow rate of a flowing fluid due to formation of boundary
layer.
2. Momentum Thickness (θ) :
It is defined as a distance measured perpendicular to the boundary of a
solid body, by which boundary should be displaced to compensate for
reduction in momentum of a flowing fluid due to formation of boundary
layer.
3. Energy Thickness (δ**):
It is defined as a distance measured perpendicular to the boundary of a
solid body, by which boundary should be displaced to compensate for
reduction in kinetic energy of a flowing fluid due to formation of boundary
layer.

34. Numericals on Boundary Layer Theory:

37. 2. Forces on Submerged bodies
(Lift and Drag Forces on the body)

39. Numericals on Lift and Drag-

42. 3. Separation of Boundary layer

43. Conditions of Separation of Boundary layer
• If you recall the relation for laminar flow between
two parallel plates, we have,
• In above expression, the thickness t is infinite as
there is only one bottom plate and no other plate,
hence the term (t-2y) will be always positive and
hence will be negative if is positive and vice-
versa. In short & are having inverse
relationship with each other.

44. • Hence the three conditions of Separation of
Boundary layer are as follows:
1. If > 0 at y=0 i.e. < 0 – Not Separated.
2. If = 0 at y=0 i.e. = 0 – about to Separate.
3. If < 0 at y=0 i.e. > 0 – Separated.

45. Numericals on Separation of Boundary layer-

48. Thank You