# math

posted by on .

Take the greatest care with your significant digits. If you don’t, this question is not “do-able”.
Llyn y Gweision (a Welsh lake) has a surface area of 10 km2. It is fed by two rivers: the Afon Chwefru and the Nant Aeron. The Chwefru has a catchment area of 1250 km2. The Aeron has a catchment area of 2.400 * 106 ha. The outflow stream, the Afon Rhondda has an average annual flow rate of 1367.6 ft3 s-1 (c.f.s). Rainfall in the region is 40.0 inches y-1, and annual evaporation from the lake surface is 8.10 * 106 m3.The equilibrium amount of water stored in the lake is 0.550 km3. Of the total amount of rainfall over the Chwefru basin, 32.0% leaves the basin as streamflow. For the Aeron basin, the annual streamflow amounts to an equivalent water depth of 33.87 mm over the whole basin. Show that for the above inputs and outputs that S = 0. If 10% of the flow from the Chwefru is diverted for municipal water supply, how much will lake level fall in one year; all else staying the same?
A friendly (continuity) equation might be:

(ICh+ IAe + IP(goes down) ) - (0Rh + OEv) = (delta)SL

where Ii = Inputs, Oi = Outputs and S = change in storage

conversions:
1 ha = 104 m2 (a hectare {ha} is an area 100 x 100m);
1 m = 3.2808 feet,
1 km2 = 106 m2 (103 x 103) m2;
1 inch = 25.4 mm;
1 m = 1000 (103) mm,
1” (inch) = 2.54 cm,
1 (Canadian) gallon = 4.55 L,
1 (American) gallon = 3.785L,
1 L = 1000 cm3,
1 mile = 5,280 feet,
1 mile2 = 640 acres