Manning formula

One of the best and most widely used formulas for open-channel flow is that of Robert Manning, who published it in 1890. Manning found from many tests that the value of C varied approximately as Ry< and others observed that the proportionality factor was very close to the reciprocal of n, the coefficient of roughness in the classical Kutter formula. The Kutter formula, which was for many years the most widely used of all open-channel formulas, is now of interest principally for its historical value and as an outstanding example of empirical hydraulics. This formula, which may be found in several handbooks, included terms to make C a function of S, based on some river flow data that were later proved to be in error. This led to the Manning formula, which has since spread to all parts of the world. In metric units, the Manning formula is... 

The dimensions of n are seen to be TL m. As it is unreasonable to suppose that the roughness coefficient should contain the dimension T, the Manning equation is more properly adjusted so as to contain (g)v2 in the numerator, thus yielding the dimension of Ly for n. In order to avoid converting the numerical value of n for use with English units, the formula itself is changed so as to leave the value of n unaffected. Thus, in foot-pound-second units, the Manning formula is... 

The Manning equation for uniform flow, Eq. (10.125), can be applied to nonuniform flow with an accuracy that is dependent on the length of the reach taken. Thus a long stream will be divided into several reaches, such that the change in depth is roughly the same within each reach. Then, within a reach, the Manning formula gives... 

Of course, this type of solution is not restricted to the Manning formula. Equation (10.124) may be replaced with a similar relation based on a constant value of the Chezy C or on a value that varies with R in accordance with Eq. (10.124). 

Determine the friction-head loss in 2500 ft of clean 10-in new tar-dipped cast-iron pipe when 2000 gal/min (0.126 m3/s) of cold water is flowing. What is the friction-head loss 20 years later Use the Flazen-Williams and Manning formulas and compare the results. 

Compute the friction-head loss using the Manning formula. The Manning formula is hf = n2if /(2.2()SR li ). where n = a constant depending on the condition and kind of pipe other symbols as before. 

For coated cast-iron pipe in fair condition, n = 0.013, and hj= 0.0411 ft of water. For 2500 ft of pipe, the total friction-head loss = 2500(0.0411) = 102.8 ft (31.4 m) of water, as compared with 112.9 ft of water computed with the Hazen-Williams formula. Thus the Manning formula gives results higher than the Hazen-Williams in one case and lower in another. However, the differences in each case are not excessive (73.8 — 65.9)/65.9 = 0.12, or 12 percent higher, and (112.9 — 102.8)/102.8 = 0.0983, or 9.83 percent lower. Both these differences are within the normal range of accuracy expected in pipe friction-head calculations. 

The Manning formula can be derived from the Chezy formula by assuming that / is inversely proportional to Ri. The roughness factor n can be taken as 0.012 for reasonably smooth steel pipes when SI units are used. For the case above... 

The Manning formula represents an attempt to refine the Chezy equation in terms of the constant C ... 

Now that a flow rate of 2.56 cfs has been established, the actual line calculations can be developed through the use of graphs based on the Manning formula, illustrated in Exhibit 13-13. First, a line is drawn... 

FLOW FOR CIRCULAR PIPE FLOWING FULL BASED ON MANNING FORMULA (n=0.013)... 

Figures 6-12 and 6-13 clearly demonstrate that it may be erroneous to use conventional Manning formulae for water flow depending on the roughness of the pipe, as these ignore the resultant roughness due to sand dunes and anti-dunes. Figures 6-14 and 6-15 clearly in-...

Chezy formula A semi-empirical formula that relates the rate of discharge of liquid in an open channel to its dimensions, slope, and surface roughness as Q = CA-JrM where C is the Ch zy coefficient, A is the cross-sectional area of the channel, m is the mean hydraulic diameter, and i is the slope of the channel. The formula was devised by French engineer Antoine Ch zy (1718-98) who was responsible for designing a canal system to supply water to Paris. The Ch zy coefficient was developed further in 1890 by Irish engineer Robert Manning (1816-97). See manning formula. 

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