By Faith A. Morrison
This can be a sleek and chic advent to engineering fluid mechanics enriched with quite a few examples, workouts, and functions. it's according to religion Morrison's imaginative and prescient that flows are either attractive and intricate. A swollen creek tumbles over rocks and during crevasses, swirling and foaming. Taffy may be stretched, reshaped, and twisted in a number of methods. either the water and the taffy are fluids and their motions are ruled by way of the legislation of nature. The target of this textbook is to introduce the reader to the research of flows utilizing the legislation of physics and the language of arithmetic. this article delves deeply into the mathematical research of flows, simply because wisdom of the styles fluids shape and why they're shaped and the stresses fluids generate and why they're generated is key to designing and optimizing smooth structures and units. innovations similar to helicopters and lab-on-a-chip reactors may by no means were designed with out the perception introduced by way of mathematical versions.
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Note that in the correlations there are different values of K f depending on whether the flow is laminar or turbulent. Also, the v j used in the summation over the straight-pipe segments is the average velocity in the straight pipe, which is different for different values of D j . 124 for the friction term in piping systems, we now are ready to calculate a mechanical energy balance with friction. 6. The following example uses this procedure. 10. 17? Do not neglect the effect of friction. The piping may be considered to be smooth pipe.
For turbulent flow, the correlations of friction factor as a function of the Reynolds number cannot be obtained analytically but have been found through careful experiments (see Chapter 7). A useful empirical equation that fits the data for turbulent flow is the Colebrook formula , which gives f as a function of the Reynolds number and ε, a surface roughness parameter relevant for commercial pipe. 161) where D is pipe diameter. 21 on a log-log plot. 95, the Colebrook equation requires an iterative solution.
158. 95 to predict losses in long straight pipes. 8 also can be solved now that we have f (Re) (see Problem 8). 95. For Re < 2,100, f = 16/Re, which on a log-log graph is a line of slope −1. This is the Moody plot . 9. An oil pipeline carries crude oil from Northern Alaska to the year-round port in Valdez, Alaska, for shipment to refineries for processing. S. 22)? The pipe walls may be assumed to be smooth (ε = 0). 0 kg/m3 . SOLUTION. The system of oil in the pipeline is a single-input, single-output, steady flow of an incompressible fluid.