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                                         Reynold's Theory Fig: Transfer of momentum in turbulent flow Relative velocity of layer 'A' w.r.t. layer 'B' is So, fluctuating components in X and Y directions due to turbulence are Vx and Vy . Now if over a surface of area 'A' perpendicular to the Y-direction and separating two adjacent fluid layers the component 'Vy ' is uniformly distributed.  So, Mass of fluid transferred across that surface from one layer to another per second =                                                        pAVy This mass of fluid has started moving with a relative velocity 'Vx'. So, Transfer of momentum = pAVxVy takes place, resulting in developing tangential forces on each of the layers. Now, the corresponding turbulent shear stress exerted on fluid layers (  𝜏 )  = pVx Vy  Since, Vx and Vy are varying, the magnitude of ' 𝜏'  will also vary. Hence, usually the time average value of  shear stress is considered

  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. Ad: https://happyshirtsnp.com/   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 fl

  Reynold's Experiment • Osborne Reynolds (Mathematician & Physicist, UK) • In 1883, he developed a laboratory set up in which he injected Dye (i.e. a fine, threadlike stream  of colored liquid having the same density as water) at the entrance to a large glass tube through  which water was flowing from a tank .    Fig: Reynold's experiment Ad: https://happyshirtsnp.com/ • Procedure: ✓ The water from the tank was allowed to flow through glass tube into atmosphere. ✓ The velocity of flow was varied by the valve. ✓ Dye was injected into the flow through a small tube. • Observation: ✓ At the initial stage of flow, dye filament in the glass tube was in the form of straight line. This was  a laminar flow. ✓ When increasing the velocity of flow, the dye filament was no longer a straight line. The dye  filament starts to become wavy. This was a transitional flow. ✓ While further increase in velocity of flow, the wavy dye filament broke up and finally diffused in  water. This was a

                               PIPE FLOWS Introduction to Pipe Flow Introduction • Hydraulics deals with both internal as well as external flow. • Internal flow and External flow: Internal flow is also known as bounded flow. Pipe flow such as water supply system, irrigation system in pipe. Open channel is a part of internal flow. External flow: Fluid flow around turbines, blades, automobiles, building, bridge abutments etc. In both case of flow, no slip condition will take place. A pipe is a closed conduit having circular X-section, used for carrying fluid under pressure. When pipe is running full of liquid, flow is under pressure.  Frictional resistance: Fluid flowing in a pipe is always subjected to resistance due to shear force between fluids particles and the fluid boundary wall of the pipe and between the fluid particles themselves resulting from the viscosity of fluid. So, there is always be loss of energy in the direction of flow which depends on type of flow such as laminar

Read more: Pipe flows and open channel flows in Hydraulics Reynold's Experiment | Laminar flow's in circular pipe | Shear stress distribution Interception and Interception losses

  INTERCEPTION   When rainfall occurs over catchment areas some of the amount of water might be lost be cause of vegetation cover and then evaporation occurs. The amount of water which is evaporation due to vegetation cover is called interception. About 10 to 20% of the total rainfall are lost due to interception. When the water retained by vegetation cover evaporated and reaches to atmosphere, then the process is called interception losses. It’s very difficult to measure the amount of water intercepted during rainfall and storms. It mostly depends upon the extent of vegetation cover and also on the velocity of wind during the rainfall (Storms). If the area is experiencing a large number of storms, then interception losses is quite large due to the forest losses and accounts for about 20% of the total annual precipitation. Interception losses are observed to be larger for the small storms as shown in fig below and smaller as the rainfall precipitation increases.  Ad: https://happyshirt

Texture is defined as the size, shape and arrangement of the grains of crystals in a rock.  Igneous rock can have different textures depending on different bases: On the basis of degree of crystallization:       All of the minerals present in the rock may be distinctly crystallized and may be easily recognized by unaided eye or they may be very poorly crystallized or even glassy (i.e. non crystallized) Polycrystalline (Phaneric/ Phanerocrystalline) : When all the minerals are distinctly crystallized.    Holohyaline (Aphanitic): when the component minerals are very fine in size and glassy or non-crystalline in character. Merocrystalline : intermediate type of texture i.e. some minerals are crystallized and others are of glassy characters. b ) On the basis of granularity: Granularity defines the grain size of rocks taking into account the average dimensions of different component minerals. The rock is described as:   Coarse grained : If the average size of the minerals of the rock