The major part of the data analysis is to develop a relation between both the renowned equations. Hence, the values of head loss per unit length of a plastic pipe obtained from all the five models were plotted as shown in Fig.
It is observed that the values are very precise and close to each other, and they follow a certain pattern. A trend line was plotted for the scatter plot whose equation came out to be:. The R 2 value for the trend line was found to be 0. This is further substantiated by the residual plots Fig.
These values were traced to be for 50 mm diameter pipe. Though the deviation is negligible in this case, it can be deduced that with the increase in pipe diameter and flowrate, the head loss value would deviate more from the trend line. Hence the present empirical relationship should be considered valid to a maximum of 50 mm diameter of plastic pipes.
Furthermore, the calculated values of f and R e were plotted as in Fig. This shows that the manual calculations performed for the DW equation are good and perfectly reliable to be used for developing correlation with HW equation. The unique feature of this relationship is that it can be used to determine the head loss obtained by DW equation directly without calculating the friction factor and Reynolds number when the corresponding value by HW equation for similar flow parameters is available.
This feature makes the task easy for pipe manufacturers and related industry. However, for larger flows and larger diameters, the values are found to significantly deviate from the trend line, which marks the limit of the proposed correlation. Reviewer: Is the developed relation valid in extreme conditions e. Authors: Steel pipes in general have a very high rate of thermal conductivity, and according to a few studies, the temperature of the external surface of a metallic pipe is the same as that of the water flowing inside it.
It is seen that, the change in the temperature of water caused by the extreme weather conditions remains within the temperature range considered for this study. Moreover, as a protective measure, water supply pipes are provided with thermal insulations throughout their lengths to deny any effect of external temperature on the temperature of water inside the pipe resulting in further decrease in the difference in temperature.
Hence it can be said with confidence that the developed relation is equally valid for extreme weather conditions. Authors: For other materials of water supply pipes the difference in the calculated head loss values is found to be huge. Figures developed for GI pipe, mentioned below, can be viewed in conjunction with Fig. The developed relation is only valid for plastic pipes which are more commonly used and have a lot of benefits over other pipe materials.
The research can be extended at later stage to study the effects caused by other pipe materials. Valiantzas, Journal of Irrigation and Drainage Engineering, 4 : Yildirim G Computer-based analysis of explicit approximations to the implicit Colebrook—White equation in turbulent flow friction factor calculation, Advances in Engineering Software, 40 — It is based on a balance of driving forces from pressure gradient and slope compared with the viscous and drag forces that restrict flow.
Where h is head loss, f is friction factor, L is length, D is diameter, V is velocity and g is gravity coefficient. The Darcy-Weisbach equation dates to the midth century. The Darcy-Weisbach equation uses a friction factor, f, to account for all the things that affect head less. It took many years to develop formulas for calculating f, because the behavior of the boundary layer depending on whether the boundary layer was smooth or rough.
It took some insightful researchers to realize that what was happening at the boundary layer between the conduit and the fluid was crucial in determining head loss. It took a lot of experiments by researchers like Johan Nikuradse and others t understand what controlled f. Numerous other researchers extended the range of Reynolds Numbers and roughness, and eventually Colebrook and White came up with the equation for determining f. This was difficult for manual calculations, so a Princeton Professor, Lewis Moody, came up with the now infamous for students Moody diagram in the s.
Hello Anna, Please share your model files for testing. Refer the link below to send model files. Anna, since these two different friction methods utilize two different types of friction factors, they cannot necessarily be compared "apples to apples" - a Hazen Williams C of might not provide the Up 0 Down Cancel. Thanks, Mal. The problem is that they are set to Water20C , so they should be the same. Maybe there somewhere else I can look?
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