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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

  Minor head losses in pipes When velocity of flowing liquid changes (either in magnitude or in direction) then there is minor losses in head (Energy) which is called minor head losses in pipes . In case of long pipes these losses are usually quite small as compared with the loss of energy due to friction and hence these are termed as 'Minor head losses' which may even be neglected without serious error, however, in short pipes these losses may sometimes outweigh the friction loss. In addition, minor head losses are negligible when they include only 5% or less of the friction head loss, So, it can be concluded that minor head losses are significant for short pipes only. Ad: https://happyshirtsnp.com/ Types of minor head losses There are different causes of minor head losses; some of them are discussed below. i)Head losses due to sudden expansion of pipe: Let us assume that liquid is flowing through the pipe from section 1 to section 2 where there occur

                               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