A lake is 12 km in length by 2.5 km in width. The inflow for the month of April is 3.26 m3/s and the outflow is 2.93 m3/s. The total monthly precipitation is 15.2 cm and the evaporation is 10.2 cm. The seepage out of the lake is estimated to be 2.5 cm. Estimate the change in storage during the month of April. (5 points)

The volume of water in the lake increases by 1605360 m³ and the water level rises by 5.35 cm

Explanation:

The total change in volume of water in the lake for April will be

(Amount of inflow to the lake - Amount of outflow from the lake) + Amount added by precipitation - Amount removed by evaporation - Amount lost by seepage

There are 30 days in April, 30 days = 30 × 24 × 3600 = 2592000 seconds

Amount of inflow to the lake = 3.26 × 2592000 = 8449920 m³

Amount of outflow = 2.93 × 2592000 = 7594560 m³

The total precipitation = Surface Area of the lake × depth of precipitation = 12 km × 2.5 km × 15.2cm = 12000 × 2500 × 0.152 = 4560000 m³

Total amount lost by evaporation = 12000 × 2500 × 0.102 = 3060000 m³

Total amount lost by seepage = 12000 × 2500 × 0.025 = 750000 m³

Total change in volume of water in the lake for April = (Amount of inflow to the lake - Amount of outflow from the lake) + Amount added by precipitation - Amount removed by evaporation - Amount lost by seepage

= 8449920 - 7594560 + 4560000 - 3060000 - 750000 = 1605360 m³

The water in the lake increases by a volume of 1605360 m³

To find the increase in height of water level,

Volume = length × width × height

Height = volume/(length × width) = 1605360/(12000 × 2500) = 0.0535 m = 5.35 cm

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