Turbulent Flow | Velocity and shear stress in turbulent flow

Turbulent Flow in Circular Pipe

• In laminar flow ( <2000) any disturbance produced is quickly damped out by the viscous resistance.

• At higher Re (Re>4000), the fluid motion is irregular and random. There is complete mixing of fluid due to collision of fluid masses with each other. The resulting flow is known as turbulent flow. The phenomenon of turbulent motion is known as turbulence.

• In turbulent flow, velocity fluctuation causes a continuous interchange of fluid masses between neighboring layers, which is accompanied by a transfer of momentum. This momentum transfers results in developing additional shear stress besides viscous shear stress. The additional shear stress is known as turbulent shear stress.

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Velocity in turbulent flow

In turbulent flow, velocity does not remain constant with time. The velocity at any instant is considered to be made up of a mean value and a fluctuating component.

Fig: Velocity variation in turbulent flow

Over large time 'T', mean of fluctuating component = 0 & the mean value is taken for computation purpose.

Similarly, in other directions,

v(t) = v + v' and w(t) = w + w'

Fluctuating component = mean velocity of layer 1- mean velocity of layer 2

Features of Turbulent Flow in Pipe

Fig: Comparison of velocity profile for laminar and turbulent flow

•Flatter velocity (more uniform) profile due to mixing of fluid layers and exchange of momentum
•Large velocity gradient (du/dy) near the wall resulting in more shear
•Additional shear stresses due to turbulence
•Higher frictional loss due to the formation of eddies, mixing and curving of path lines.

Shear stress in turbulent flow

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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

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

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).

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