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  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

  Moody's Diagram (or Moody's Chart) Fig: Moody's diagram for the friction factor 'f' for commercial pipes-I L.F. Moody has plotted the equation as shown in above figures, commonly known as 'Moody Diagram' which is essentially the same as thet of Nikuradse's plot except for the transition regions. So, 'Moody chart' is the chart of friction factor 'f' versus 'Re' curves for various values of 'R/k'. For any turbulent pipe flow problem the value of friction factor (f) can therefore be determined from Moody's Diagram  if the numerical values of 'R/k' for the pipe and 'Re' of flow are known. The values of 'k' which may be adopted for the pipes of some of the common materials are given below Ad: https://happyshirtsnp.com/ Fig: Moody's diagram for friction factor 'f' for commercial pipes-II The value of Equivalent sand grain roughness (k)' given in Table 1-2 correspond to material in ne

  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