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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

  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