An open channel is to be constructed from a relatively flat plain, it is designe
ID: 1920473 • Letter: A
Question
An open channel is to be constructed from a relatively flat plain, it is designed to carry 600 cfs tor 280 days during the year. The canal is designed to be hydraulically most efficient, it is decided to use a trapezoidal shape with side slopes of 2 horizontal to 1 vertically. The canal can be excavated at a price of $0.50 per cubic yard. A concrete lining, if provided, will cost $1.30 per square yard. Annual maintenance cost of the unlined canal is $1000 per mile. Maintenance charges of $2500 every 5 years are estimated for repair of lined canal. If the interest rate is 6%, the life of either alternative is 50 years, the estimated seepage loss from the unlined canal is 1 ft3/ ft2/day and the price of water is $5.00 per acre ft. Land slope = 0.0026, freeboard = 1 ft, thickness of concrete lining = 0.20 ft. n for lined canal 0.014, n for unlined canal 0.018. (1 yard = 3 ft.) Compare the total annual cost of the two systems (lined & unlined canal) From what you computed, which item is the most significant item in cost saving? How would you improve the design of the less effective system to make it competitive? If we include the cost of evaporation lost, would the conclusion be any different?Explanation / Answer
manning's equation: Q=A.(R^(2/3)).(s^0.5)/n
for lined canal, A*(R^(2/3)) = 600*0.014/(0.0026^0.5) = 164.74
for unlined canal, A*(R^(2/3)) = 600*0.018/(0.0026^0.5) = 211.81
for most efficient trapezoid canal,
R = h/2,
A = h2(2((m2+1)^0.5)-m) = 2.47 m
--> A*(R^(2/3)) = 0.78*(h^(8/3))
(a) 1.) for lined canal,
0.78*(h^(8/3)) = 164.74
h=7.45 ft
total height including freeboard and lining thickness = 7.45+1+0.2 = 8.65 ft
Cost:
excavation = (0.5/3)*2.46*(h^2) = $30.8
concrete lining: = (1.3/9)*(A/r) = (1.3/9)*4.94*h = $6.17
maintainance = 2500/5280 = $0.47 per 5 year
total cost = 30.8+6.17+0.47*(p/A,6%*5,50/5)
= 30.8+6.17+0.47*(1.310-1)/(0.3*(1.310)
= 30.8+6.17+14.53 = $51.5
2.) for unlined canal:
0.78*(h^(8/3)) = 211.81
h=8.18 ft
total height including freeboard and lining thickness = 8.18+1+0.2 = 9.38 ft
Cost:
excavation = (0.5/3)*2.46*(h^2) = $36.22
concrete lining: = $0
maintainance = 1000/5280 = $0.189 per year
cost of water lost from seepage = 1*A/r*5/43560*365 = $1.94 per year
total cost = 36.22+(0.189+1.94)*(p/A,6%,50)
= 36.22+(0.189+1.94)*(1.0650-1)/(0.06*(1.0650)
= 36.22+33.56 = $69.78
thus, the lined canal would cost $51.5 at construction whereas unlined canal would cost $69.78.
(b) the concrete lining is the most significant item in cost saving.
(c) the side slope of the unlined canal can be reduced from 2h:1v to say, 3h:1v.
this would decrease the height required by the canal to 5.6ft. this would significantly reduce the cost of excavation and also seepage loss as the former is directly proportional to the square of the height of canal and the latter is directly proportional to the height of canal.
the final cost of the unlined canal would then be = $44.9
(d) No, our conclusion would be the same even if we consider the cost due to evaporation. evaporation would be almost same for both the canals and thus would not make much difference in the cost estimate of the two canals.
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