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' Î± 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

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

Water hammer and unsteady flows in pipes

             Ad: https://happyshirtsnp.com/                                                                             UNSTEADY FLOW IN PIPES When water is flowing through a pipe is suddenly stopped by the use of valve then we can see sudden rise in pressure inside the pipe and this pressure waves transmitted along the length of the pipe and it creates knocking like sound effects knows as 'water hammer'. In doing so, there are rapid pressure oscillation in the pipe, often accompanied by a hammering like sound, this phenomenon is called as 'Water hammer effect'. Sometimes the pressure may rise to the greater extent and may causes serious damage to the pipe. Therefore the 'water hammer' effects should be properly studied in the pipes. The magnitude of pressure rise depends on:   i)    Speed at which the valve is closed   (ii)     The velocity of flow (V) (iii)     The length of the pipe (L) (iv)      Elastic properties of pipe material (E) and flowing fluid (K).
Post a Comment
Read more

THREE RESERVOIRS AND PIPE NETWORK PROBLEMS

 Ad: https://happyshirtsnp.com/         THREE RESERVOIRS PROBLEM AND PIPE NETWORK   In practice, several pipes are interconnected forming various loops (or circuit) in municipal water distribution systems. There are a number of pipes connected either in series or in parallel or a combination of both. A group of interconnected pipes forming several loops (or circuit) in complex manner is called pipe networks, The complexity in a pipe networking is to determine the solution Of pipe problem (flow distribution) in such pipe network. Branched pipes: Three Reservoirs Problem Fig: Branched pipes: three inter connected Reservoir     In water supply system, Often a number of reservoirs are required to be interconnected by means Of a pipe system consisting of a number of pipes namely main and branches which meet at a junction. Figure shows three reservoirs 'B' and 'C' are interconnected by pipes 'a', 'b' and 'c' which meet at a junction 'D'. In the
Post a Comment
Read more