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Using dimensional analysis, it can be shown that [9] ' D ' D ' in which 0 represents a function of. As it is extremely difficult to quantitatively consider the effect of e' and m, their effect is either ignored or is included indirectly by considering equivalent size e. 1) can be reduced to The term VDQ//JL is the Reynolds number Re. The dimensionless parameter elD is known as the relative roughness. 2) can be written as J. 4). As H. P. G. 4). 4) is now commonly known as the Darcy-Weisbach formula.

6), the head loss h, is determined. 008 Pa • s) flows through a 100-mm diameter, 5-km long pipeline at a rate of 5 m3/h. Find the head loss due to friction. 302 860 Q x 1 0 - nWs Since Re < 2000, the flow is laminar. 2 Water flows through a 300-mm diameter, l-km long new cast iron pipe. 1 m3/s, determine the head loss in the pipe by all three head loss formulas. Solution 1. 26 mm. 667 x 10"4 300 Taking v — 1 X 10~6 m2/s for water, «' - ^ " , x 0 4 3 X x°,'x . 01974. 714 m; from the Haaland relationship, Equation ( 2 .

In transitional turbulent flow, the value of/depends on both Re and elD. (5) For very large values of Re, the effect of viscosity is negligible, and /becomes independent of Re and remains constant for a particular value of elD. This flow is termed rough turbulent flow and /depends only on the elD value. Stanton, in collaboration with Pannell, conducted experiments on several pipes of different diameters and materials using several fluids. 1 is sometimes known as the Stanton diagram or the Stanton-Pannell diagram.

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Analysis of Flow in Water Distribution Networks by Pramod R. Bhave

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