With the increasing use of pipe lines for oil transport in the petroleum industry, mathematical calculation of design is essential. The equations connecting the variables involved in fluid flow, however, are complicated and the solution of such equations might prove cumbersome to a non-mathematical man. A nomograph enables such complicated equations to be solved graphically, and it is for this reason that the following nomo graph has been presented. The well-known equation for fluid flow, la = j '-can be written 2 gm.. where P = friction head in lbs. per sq. inch. S = specific gravity of the fluid. l= length of line in miles. Q = quantity of oil to be pumped in barrels per hour. d = diameter in inches. v = kinematic viscosity in C.G.S. units. deduced by O. Wolfe for the turbulent range is as follows 1 0463 = 044 -\- 1047 ~~)....(2) vd Although other equations of the simple index type have been suggested for f it is believed that these are a special case of the law of the form f = a +bx" and hence the adoption of formula (2) will represent the variation of f more accurately. Substituting (2) in (1). P0-44SIQa10-47;0-46 SlQi.54 = ds +d4.54 or The friction factor f is a function of \R\ and its value as s Q5 = 0-44(9)s + 10-47(4)4.54 This can be written Sqa0-44(d)5+ 10-47(d)4.54.... (4)
Neverthelesss, any fundamental formulae for determining the flow of viscous fluids must, however, be based on hydrodynamic principles. Prior to the work of Osborne Reynolds the results of experiments carried out by hydraulic investigators have led to a vast number of empirical formulae, and these formulae have been accepted as a basis for design. This necessitated the determination of new constants by trial and error for the application of these empirical formulae, when problems connected with the pumping of a fluid other than water were involved. Consequently, this procedure led to confusion and considerable inaccuracy. During the past century, researches by Poisieulle, Stokes, Osborne Reynolds, Rayleigh, Stanton and Pannell, and a number of other scientists, have placed the fundamental .laws of fluid flow in a position in which they are more or less applicable to all kinds of fluids flowing through circular pipes having all types of surfaces. As a result of these studies a general relation applicable to all fluids and conditions of flow was predicted. Although it was established. that two modes of flow existed, namely, streamline and turbulent, it was not until Reynolds had investigated this obscure matter that an explanation was forthcoming. The introduction of streams of coloured liquid into the main stream of water flowing through a glass pipe showed that two types of flow could occur even in the same pipe.