Flow in a Pipe of Rectangular Cross-Section
Proceedings of the Royal Society A
List of Symbols, a = half w idth of pipe in centim etres. b = hah depth of pipe in centim etres. m = hydraulic mean depth = -T . a + b p = pressure. Q = quan tity of water in cubic centim etres per second. R = resistance per u nit area in dynes per square centim etre. S = average velocity in centim etres per second. . t = tem perature. w = velocity of a particle parallel to the axis of the pipe. 2 = distance parallel to the axis of the pipe, p = density. H = absolute viscosity. v -kinem atic
... cosity. Note,-R X (area of walls) = (difference of pressure) X (area of cross-seotion). Hence R . 4 (a + b) dx = -dp . 4ab ; or R = -m . dz Object of Research , The object of the research was to investigate the flow of water in a pipe of rectangular cross-section. Much work has been done on similar problems with pipes of circular section,* and pipes of rectangular section have been investi gated by Frommf and Davies and White. J Fromm worked with pipes in which the ratio of the sides was never less than 6 to 1 ; his report deals only with turbulent flow. In the case of Davies and White's research, the minimum ratio of the sides was 40 to 1, so that the laminar flow could be calculated from the formula for flow between infinitely wide parallel plates. The present writer used a pipe of section 1*178 cms. by 0*4:04 cms. (ratio of sides = 2*92) ; this presents a fresh problem where stream line flow is concerned, and shows interesting results in the region of the critical velocity.