Turbulent flow

It is based on fluid mechanics

1. Gandhinagar Institute of Technology Subject :- Fluid Mechanics Prepared By – Pavan Narkhede [130120119111] Darshit Panchal [130120119114] Topic :- Turbulent Flow Guided by : Prof.Jyotin kateshiya MECHANICAL ENGINEERING 4 th - B : 2

2. INTRODUCTION: Laminar Flow : In this type of flow, fluid particles moves along smooth straight parallel paths in layers or laminas, with one layer gliding smoothly over an adjacent layer, the paths of individual fluid particles do not cross those of neighbouring particles. Turbulent Flow : In turbulent flow, there is an irregular random movement of fluid in transverse direction to the main flow. This irregular, fluctuating motion can be regarded as superimposed on the mean motion of the fluid.

3. Laminar Transitional Turbulent

4. Types of flow depend on the Reynold number , ρ Vd Re = -------- µ Re < 2000 – flow is laminar Re > 2000 – flow is turbulent 2000 < Re < 4000 – flow changes from laminar to turbulent.

5. Magnitude of Turbulence : It is the degree of turbulence, and measures how strong, violent or intence the turbulence. - Magnitude of Turbulence = Arithmetic mean of root mean square of turbulent fluctuations = =

6. Intensity of turbulence : - It is the ratio of the magnitude of turbulence to the average flow velocity at a point in the flow field - So, Intensity of Turbulence =

7. Expression for co-efficient of friction : Darcy – Weisbach equation From the experimental measurement on turbulent flow through pipes, it has observed That the viscous friction associated with fluid are proportional to Length of pipe (l) Wetted perimeter (P) Vn , where V is average velocity and n is index depending on the material (normally, commertial pipe turbulent flow n=2

8. f – friction factor L – length of pipe D – diameter of pipe v – velocity of flow OR

9. Moody Diagram : Developed to provide the friction factor for turbulent flow for various values of Relative roughness and Reynold’s number! From experimentation, in turbulent flow, the friction factor (or head loss) depends upon velocity of fluid V, dia. of pipe D, density of fluid ρ , viscosity of fluid µ, wall roughness height ε . So, f = f 1 (V,D, ρ , µ , ε ) By the dimensional analysis, , Where called relative roughness.

10. Key points about the Moody Diagram – In the laminar zone – f decreases as Nr increases! 2 . f = 64/Nr. 3 . transition zone – uncertainty – not possible to predict - 4. Beyond 4000, for a given Nr, as the relative roughness term D/ε increases (less rough), friction factor decreases

11. 5. For given relative roughness, friction factor decreases with increasing Reynolds number till the zone of complete turbulence 6. Within the zone of complete turbulence – Reynolds number has no affect. 7. As relative roughness increases (less rough) – the boundary of the zone of complete turbulence shifts (increases)

12. Co-efficient of friction in terms of shear stress : We know, the propelling force = (p1 - p2) Ac ---- (1) Frictional resistance in terms of shear stress = As Where = shear stress ----(2) By comparing both equation, (P1 – P2) = OR ( co-efficient of frictionin terms of shear stress)

13. Shear stress in turbulent flow In turbulent flow, fluid particles moves randomly, therefore it is impossible to trace the Paths of the moving particles and represents it mathematically

14. = mean velocity of particles moving along layer A = mean velocity of particles moving along layer B = - Shear stress in turbulent flow It is the shear stress exerted by layer A on b and known as Reynold’s stress.

15. Prandtl’s mixing length theory : Prandtl’s assumed that distance between two layers in the transverse direction (called mixing length l) such that the lumps of fluid particles from one layer could reach the other Layer and the particles are mixed with the other layer in such a way that the momentum of the Particles in the direction of x is same, as shown in below figure :

16. Total shear where , (Viscosity) n = 0 for laminar flow. For highly turbulent flow , .

17. Hydrodynamically Smooth and Rough Pipe Boundaries Hydronamically smooth pipe : T he hight of roughness of pipe is less than thickness of laminar sublayer of flowing fluid. K < δ′ Hydronamically rough pipe : The hight of roughness of pipe is greater than the thickness of laminar sublayer of flowing fluid. K > δ′

18. From Nikuradse’s experiment Criteria for roughness : Hydrodynamically smooth pipe Hydrodynamically rough pipe Transiton region region in a pipe In terms of R eynold number If Re → Smooth boundary If Re ≥100→Rough boundary If 4<Re <100 →boundary is in transition stage.

19. The Universal Law of The Wall

20. Velocity Distribution for turbulent flow Velocity Distribution in a hydrodynamically smooth pipe Velocity Distribution in a hydrodynamically Rough Pipes

21. Velocity Distribution for turbulent flow in terms of average Velocity (V) Velocity Distribution in a hydrodynamically smooth pipe Velocity Distribution in a hydrodynamically Rough Pipes

22. Resistance to flow of fluid in smooth and rough pipes The frictional head loss Where f = frictional co-efficient or friction factor Pressure loss in pipe is given by

23. From experimental result, the pressure loss is the function of l/D to the first power - But friction factor - From equation ,the friction factor f is a function of Re and ratio of ε /D.

24. For laminar flow We know, in laminar flow the f is function of only re and it is independent of ε /D ratio. For terbulent flow In terbulent flow, f is a function of Re and type of pipe. So f is also depend on boudary. Smooth pipe Rough pipe

25. (a) Smooth pipe For smooth pipe ,f is only a function of Re. For 4000<Re< laminar sublayer ( δ′ >> ε ). The blasius equation for f as ,For 4000<Re< laminar sublayer in smooth pipe. From Nikuradse’s experimental result for smooth pipe

26. (b) Rough pipe In rough pipe δ′ << ε , the f is only function of ratio ε /D and it is independent of Re. From Nikuradse’s experimental result for rough pipe

27. THANK YOU….