Skip to main content

Velocity distribution in smooth pipes | Velocity distribution in rough pipes

 Velocity distribution in smooth pipes 

In the vicinity of a smooth boundary there exists a laminar sublayer. The flow in the laminar sublayer being laminar has a parabolic velocity distribution. Since the thickness of laminar sublayer (δ') is generally very small, the parabolic velocity distribution in the region may be approximated by a straight line without appreciable error. 

So, in the zone of laminar sublayer, since the flow is laminar, the viscous stress predominates and the turbulent stresses tend to become zero. Therefore, in the laminar sublayer, the shear is 




For linear velocity distribution within the laminar sublayer, 'du/dy' becomes 'u/y'.


Ad:





Fig: Velocity distribution for turbulent flow near a smooth boundary

Furthermore, if it is assumed that in the laminar sublayer, i.e. up to y=δ', 'τ' remains constant and equal to 'τo'. The shear stress at the pipe boundary is
Which is the velocity distribution laminar number sublayer, i.e. form y=0 to y=δ'. Here, term (u* y/u) is dimensionally to a form of Reynold's number
 Form Nikuradse's experiment of turbulent flow in smooth pipe,


Which represents the velocity distribution in the region of turbulent flow near hydrodynamically smooth boundaries and it is applicable for regions outside the laminar sublayer i.e. y≥δ'.

Velocity distribution in rough pipes

The flow condition near hydrodynamically rough boundaries are different from that of hydrodynamically smooth boundaries. This is so because in the case of rough boundaries the surface irregularities protrude well behind the laminar sub layer, which is therefore is completely destroyed as shown in fig. As such velocity distribution in turbulent flows near hydrodynamically rough boundaries is considerably affected by the surface protrusions eqn applies equally to the turbulent flow in hydrodynamically rough pipes.
In order to obtain the equation which would represent the velocity distribution for turbulent flow near hydrodyamically rough boundaries is considerably affected by surface protrusions(k),  y' must be evaluated in terms of the average height of the surface
protrusions (k).
So, from Nikuradse's experiment for rough boundary, y' α k, :. y' = k/30
Fig: Velocity distribution for turbulent flow near rough boundary
Which represent the velocity distribution for the turbulent flow near hydrodynamically rough boundary.

Ad:




READ MORE


Labels:
Location: Kathmandu 44600, Nepal

Comments

Post a Comment

Popular posts from this blog

Use of double mass curve analysis | Test for the consistency of records (Double mass curve)

Use of double mass curve analysis The double mass curve is used to check the consistency of many kinds of hydrological data by comparing data for a single station with that of pattern composed of the data from the several other station in the area. The double mass curve can be used to adjust inconsistent precipitation data. The theory of double mass curve is based upon the fact that a plot of the two cumulative quantities during the same period exhibit a straight line so long as the proportionality between the two remains unchanged and the slope of the line represent the proportionality. This method can be smooth at a time series and suppress random elements in the series. In recent 30 yrs, Chinese scholars analyzed the effects of soil and water conservation measures and land use/cover changes on runoff and sediments using double mass curve method and have achieved the good results. In this study, double-mass curves of precipitation vs sediments are plotted for the two contrastive peri...
Post a Comment
Read more

Nikuradse experiment | variation of frictional factor (f) for laminar and turbulent flow

  Nikuradse', a German Engineer, He by gluing uniform sand grains on the inner side of the pipe wall to artifically roughened the pipe conducted a series of well- planned experiments on pipes. Here we choose the pipe of different diameter (D) and by changing the size of sand grain which gives (Roughness height= k), We can observe from his experiment that value of (k/D) varies from about "1/1014 to 1/30"  Since from dimensional analysis 'f is the function of Reynold's no VD/ ν  and ratio of 'k/D' Where, k =Average roughness height of pipe wall, D= Diameter of pipe,   ν = Kinematic viscosity of flowing fluid, Re =VD/ ν  = Reynold's no, k/D = Relative roughness.  Sometimes, "k/D" is also replaced by "R/k" Where, R= Radius of pipe and (R/k)= Relative smoothness whose value varies from "15 to 507''. Ad: Change(Variation) of friction factor for laminar flow (Re<2000) Head loss in laminar flow (i.e. Hagen-Poisseullie equati...
Post a Comment
Read more

Hydrodynamically smooth and rough boundaries | Velocity distribution for turbulent flow

 Hydrodynamically smooth and rough boundaries Fig: Definition of smooth and rough boundaries In general, a boundary with irregularities of large average height 'K' on its surface is considered to  be a rough boundary and one with smaller 'K' value is considered as a smooth boundary. ✓ However, for a proper classification of smooth and rough boundaries, the flow and fluid characteristics are required to be considered in addition to the boundary characteristics. ✓ As the flow outside the laminar sub-layer is turbulent, eddies of various sizes are present which try  to penetrate through the laminar sublayer. But, due to greater thickness of laminar sub-layer ,   eddies can't reach the surface irregularities and thus the boundary acts as a smooth boundary. Such  a boundary is termed as " Hydro-dynamically Smooth Boundary" ✓ With the increase in Reynold's no (Re), the thickness of the laminar sub-layer  decreases and it's  can even become much smaller ...
Post a Comment
Read more