EXAMPLE 2.7.6

Gomer has noticed that when a garden hose is left exposed to the summer sunshine, the water resting within the hose becomes heated. This inspires Gomer to construct a low-tech solar water heater. He reasons that if he connects a sufficient length of hose and leaves it in a sunny spot, this will provide an ample supply of

hot water.

He estimates that the drum of his washing machine is a cylinder whose diameter is 17 inches and height is 10 inches. Based on that

assumption, how many lineal feet of half-inch diameter water hose would be required in order to hold enough water to fill the drum of

the washing machine?

SOLUTION

We can imagine a 1-foot length of 1/2 inch diameter hose to be a narrow cylinder the has a radius of 1/4 inch and a "height" of 12 inches. Thus we can use the formula for the volume of a cylinder to determine the number of cubic inches of water in 1 foot of hose.

If we divide this number into the volume of the washing machine drum, we will know how many 1-foot lengths of hose are needed in order to contain the same amount of water as the washing machine contains.

To find the volume (in cubic inches) contained in a 1-foot length of hose we use the formula

Volume = pi times (radius squared) times height, where

radius = .25 inches (that is, one fourth of an inch) and

height = 12 inches

So, volume = pi times (.25 squared) times 12 = 2.3562 cubic inches.

We have found that a 1-foot length of hose holds about 2.4 cubic inches of water.

Now we find how many cubic inches of water are contained in the washing machine drum. Again we use the formula for the volume of a cylinder, where r = 8.5 inches and h = 10 inches.

So, volume = pi times (8.5 squared) times 10 = 2,269.8 cubic inches.

Now, if we divide the volume of the washing machine drum by the volume of the 1-foot length of hose, we will know how many 1-foot lengths of hose are needed to hold the same amount of water as the washing machine:

(2,269.8 cubic inches) divided by (2.4 cubic inches) = 963

 It will take about 963 feet of hose in order to hold enough water to fill the washing machine. Since a 100-ft length of such hose can be purchased for less than $20 (less than $10 if we use the cheapest available), this low-tech solar water heater can be constructed for less than $200, and the installation requires nothing more than connecting the lengths of hose to one another, attaching one end to the faucet, and running the other end to the washing machine.