The Ogallala aquifer described in the Closer Look box in Section 18.3, provides 82% of the drinking water for the people who live in the region, although more than 75% of the water that is pumped from it is for irrigation. Irrigation withdrawals are approximately 18 billion gallons per day. (a) Assuming that 2% of the rainfall that falls on an area of 600,000 km2 recharges the aquifer, what average annual rainfall would be required to replace the water removed for irrigation?

Video transcript

Hey everyone, we're told a 450,000 km squared down provides 72% of water to a nearby town. The town uses 15 billion gallons of water per day, How much annual rainfall will be needed to replace the water in the dam. If 3.3% of the rainfall falls in the dam to answer this question, we want our final answer to be in inches per year. So we can first start this off by converting our values two km per year. So we're going to start off with our 15 billion gallons of water per day and converting billions into tens of the nine Next. We want to convert our days into years and we know that we have 365 days in one year. Next converting our gallons into leaders, we know that we have 3.7, L per one gallon. Next converting our leaders into cubic decima tres, we know that one leader is equivalent to one cubic meter, converting our cubic decima tres into cubic meters. We know that we have 10 to the negative third cubic meters per one cubic decimate er Next converting our cubic meters into cubic kilometers, we know that we have 10 to the nine cubic meters per one cubic kilometer and lastly plugging in our 450,000 kilometers squared, We're going to divide by 450, km2ared. Once we calculate this out and cancel out all our units, we end up with a value of 4.6056 times 10 to the negative five kilometers per one year. Now we can convert this into inches per year. We know that per one km We have 10 to the 3rd m And per one m we have 10 squared cm Next we know that we have 2.54 centimeters per one inch, calculating this out and canceling out all our units. We end up with a value of 1.8132" per year. Since our question was asking us how much annual rainfall will be needed to replace the water. If 3.3% of the rainfall falls in the dam, We have to use that 3.3%. So taking our 1.8132" per year, We're going to divide this by 3.3 over 100, which is our 3.3%. So when we calculate this out, we end up with 54.95 in per one year, which is going to be our final answer. So I hope that made sense. And let us know if you have any questions