A reservoir with a length of 20 km and width of 3 km has a flood inflow of 1000

Question

A reservoir with a length of 20 km and width of 3 km has a flood inflow of 1000 m ^ 3/s. (a) If exit flow is restricted to 500 m ^ 3/s, how fast is the water level rising in the reservoir per day? (Answer is between 0.5-1 m/day), (b) If the exit flow is a spillway that follows the formula for flow over a weir (Ch. 3), set up the mass balance equation that governs the rise of water. Will water levels rise at the same rate as in (a), at a lesser rate, or a greater rate? What three additional pieces of information would we need to solve the problem?

Explanation / Answer

a).

Input flow*t - output flow*t = storage in the reservoir

input flow = 1000 m3/s

output flow = 500 m3/s

storage of the reservoir = L*B*h = (20*3*106)*h

therefore,

Input flow - output flow = (L*B)*(h/t)

1000 - 500 = (20*3*106)*(h/t)

(h/t) = 8.33*10-6 m/s or in m/day, h/t = 0.72 m/day

hence, water lever rise 0.72 m per day.

b).

velocity of the wier,v = (2gh)

here output flow is given,Q = 500 m3/s

Q = Av = (L*h)*(2gh)

Q=500 m3/s or Q = (500*24*3600) m3/day

L = 20*103 m

g = 9.81 m/s2

therefore,

(500) = (20*106 *h)*(2*9.81*h)

after solving and converting into m/day, we get, water rise, h = 0.62 m/day

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