The outlet structure of a reservoir is used to regulate the flow of water out of the

reservoir. The discharge at the outlet orifice needs to be maintained at a specified

level. Excess variation in discharge would either cause flooding or may lead to

water scarcity on the other side of the reservoir. A nominal discharge value of

40 000 m3/s is found out to ideal for utilizing the water effectively for agriculture.

The outlet structure is a circular orifice and the design equation for discharge is

given by

whereCis the orifice coefficient, A is the area of the orifice, and g is the acceleration

due to gravity, and H is the water head in the reservoir.

Assume an orifice coefficient of 0.6 and acceleration due to gravity of

9.81 m/s2. The diameter of the orifice is adjustable and due to its huge size it

cannot be set accurately each time and so the area of the orifice varies and has

a standard deviation of 3.5. The water head in the reservoir varies depending on

the amount of rainfall received and from the historical data for the region we can

compute a standard deviation of 15 for the head. Determine the nominal values of

orifice area and head which would minimize the variation of discharge and also

achieve the required nominal value of 40 000. The maximum nominal value for

head has a constraint of 750 meters.

Solution.pdf

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