Design of open channel

Transcription

1 Design of open channel Manning s n Sides slope Seepage losses Evaporation losses Free board Data ssumptions Two unknowns b & Flow rate Q Tpe of soil Longitudinal slope S Meterlogical data (temp., wind...etc. Manning s equation Q = n R / S / nother relation between b & Best hdraulic sec. b & Non-silting non-scouring Buckl s formula Charts 5

2 6.0 Design of canals and drains cross sections Design of channel cross section means the determination of its dimensions e.g. (in case of trapezoidal section b,, and z) to conve the required discharge. The factors to be considered in the design are: the kind of material forming the channel bod which determines the roughness coefficient: the minimum permissible velocit to avoid deposition if the water carries silt or debris; the channel bottom slope and side slope and the free board. To design a canal cross section ou need the following data and assumptions:. Data. Q = discharge which can be calculated from the area served and the water dut (crop requirement, irrigation sstem: surface - drip - sprinkler ),. S = bed slope (water slope) which depends on the longitudinal bottom slope of the canal (Snoptic diagram).. The tpe of soil for the design of canal or drain. B. ssumptions:. Manning s coefficient (Roughness factor) n = 0.05 for earth canal; n = 0.06 for lined canal; n = heav weed.. Side slopes Rock nearl vertical Stiff cla /: or : Firm clae silt : Loose sand : Sand loam :. Seepage losses Where: S = 0.098C Q V 4. Evaporation losses S = losses in m /sec/km; Q = flow rate m /sec; V = mean velocit m/sec; C = 0. for cla & 0. for sand. Es = Ea * Top area mm/da/km. 6

3 Where: 5. Free board Where: Ea = Evaporation rate mm/da; Top area = T * km T = Top width F = C Y F = Free board in meter; Y = Water depth in meter; C = 0.46 if Q = 0.56 m /sec; C = 0.76 if Q = 85 m /sec. Y F Berm Free board varies from 0.5 m to.5 m depending on the size of the canal. The practice free board in Egpt = 0.5 m. The minimum radius of curvature in canal = 6. Basis of the choice of b & relationship The design procedure compute the dimension b uniform flow formula, for example, Manning s equation: Q = n R / S / Where: Q = Discharge in m /sec; n = Manning s coefficient (depends on surface roughness T/L / ); R = Hdraulic radius (L); = Cross section area; P = Wetted perimeter; S = Longitudinal slope; Z = Side slope.. Best hdraulic section (most efficient section) The best hdraulic section is that section which passes the maximum discharge at constant area. For constant Q is maximum if P is minimum. Sometimes the best hdraulic section is not the most economic section, wh? The semi-circular section gives the maximum discharge and it has the minimum wetted perimeter P, therefore, it is the best section for lined canals, (it takes minimum materials). 7

4 For rectangular section From Manning s Equation Q = n R / S / = b & P = b + Put b function of b = P = dp - = - + = 0 d b = & = b = b = Which is the relation between b & for rectangular section. Example Design a best hdraulic rectangular section lined canal to conve a discharge of 0.5 m /sec. ssume the slope 5 cm/km. Estimate the cost of lining per kilometer. ssume the cost of lining.0 m equal to 0 L.E. Solution Q = n R / S / / 0.5 = 0.06 R / For the best rectangular section b = = b = & P = 4 & R = / / / 0.5 = * 0.06 / 8/ / = = 5 / / = 8/ = 0.78 m & b =.56 m F = C 0.46 * m P =.56 + * 0.78 = 4. m 8

5 Lining area = 4. * 000 = 40 m Cost of lining per kilometer = 40 * 0 = L.E. Y The best hdraulic section for trapezoidal shape: Q = n R / S / For constant, Q is maximum if P is minimum. = b + z P b + + z b = - z = - z P - z + + z For constant z. dp - - z + + z = 0 d - b + z - - z + + z = 0 - b - z - z + + z = 0 Then the relation between b, for best hdraulic trapezoidal section is b - z + + z If z = the relation becomes b = 0.88 The hdraulic radius for this section is b z Berm R = /P b using the general relation between b & for trapezoidal section then R R b + z b + + z R = = - z + z + z - z + + z + + z - z + + z + z - z + + z + + z Best hdraulic section when z = The value of z to make P minimum: 9

6 Q P - z + + z + + z = -z + 4 z Q dp dz / z z = 0 z 0 + z 4 z = + z z = 60 o z = The best hdraulic section is hexagon. Cross section Trapezoidal Table (4) Best hdraulic section for different shapes rea Wetted perimeter P Hdraulic radius R Rectangular 4 Triangular 4 Semi-circular The best hdraulic section is good onl for small canals because the ratio between the depth and the width is not practicall accepted. The best section is not the most economical section. B. Regime - pproach Non - silting and Non - scoring sections Stable section does not need maintenance e.g. No change in the cross section area under the design flow.. Kenned Equation V = k x Where = depth of flow; V = mean velocit; k = (0.6-0.) metric units; x = coefficient depending on the tpe of soil and water = 0.9 coarse light sand soil; =.0 sand loam silts; 0

7 =.09 course silt; = 0.5 clear water; = 0.67 for average conditions.. Buckle Formula a) For irrigation canals = b s + 8 for.6 m 650 s = b for >.6 m Where s = bed slope in cm/km. Two) For deep drains = b for b m. =.75 b / for b > m. Three) For shallow drains = 0.96 b for b m. =.4 b / for b > m. Example canal conveing discharge of 0 m /sec. ssume the slope is 0 cm/km, Manning s n = 0.05, and the tpe of soil I cla side slope :. Design the canal using the following methods:. Best hdraulic section;. Kenned formula V = ;. Buckle formula. Solution Q = 0 m /sec S = 0 cm/km n = 0.05 Z = Q = n R / S / 0 = 0 = Best section P / 0*0 / -5 / b + b + () b +

8 b - z + + z b b = 0.88 () Subs. from () and () 0 = / /.88 0 = = / =.7 m & b =.6 m Check the velocit =.6 * = 8.86 m Velocit = v = Q/ = 0.54 m/sec.. Kenned / V = 0.05 R / 0 / = 0.4 R 5 0 () V = (4) divide equ & 4. = R b + b + / =.4 / R =.4.4 b +.4 = b b =.48 b =.57 0 = 0.4 * / / = 0.4 * =.9 m & b = 7.8 m. Buckle formula s = 0. 0 = 0. = 0.9 b + 4 b for >.6 m + 4 b for >.6 m (5)

9 Q = 0.05 / S b + z Solve () and (5), get b &. /