Question

Question: Hydraulic engineers in the United States often use, as a unit of volume of water, the acre-foot, defined as the volume of water that will cover 1 acre of land to a depth of 1 ft. A severe thunderstorm dumped 2.0 in. of rain in 30 min on a town of area 26 km². What volume of water, in acre-feet, fell on the town?

Short answer

Answer

The volume of water in acre-feet fell in town is$1.1\times {10}^{3}acrefeet$

Step-by-step solution

Given data

Thunderstorm dumped 2.0 in. of rain in 30 min.

Area of town is 26km² .

Understanding of the unit acre-foot.

The acre-foot is a commonly used volume unit referring to large-scale water resources, such as reservoirs, aqueducts, canals, and sewage flow capacity.As its name implies, an acre-foot is defined as the volume of an acre surface to a depth of one foot.

 Step 3: Conversion of an area of town into an acre

The area of town is, A = 26 km²

To convert the volume in acre-feet units, perform the necessary conversions.

$$\begin{gathered} \text{1km=3281ft} \\ {\text{1ft}}^2\text{=}\frac{1}{43560}\text{acre} \\ 1inch=\frac{1}{12}inchft \end{gathered}$$

Using the above conversion factors, the area of town in feet is written as,

$A=26k{m}^2\times {\left(3281\right)}^2\frac{ft2}{km2}=279.89\times {10}^{6}f{t}^2$

Now, convert the area frominto acre

$279.89\times {10}^{6}f{t}^2\times \frac{1acre}{43560f{t}^2}=6425.39acre$

Thus, the area is$6425.39acre$.

conversion of height in ft.

The height of the rainfall is,h= 2.0 inch

Now, convert height from inch to ft.

$$\begin{gathered} h=2inch\times \frac{1ft}{12inch} \\ =\frac{1}{6}ft \end{gathered}$$

Thus, the height of the rainfall is $\frac{1}{6}ft$.

Determination of volume of water 

Volume of water fall is calculated as:

$$\begin{gathered} V=A\times h \\ =6425.39acre\times \frac{1}{6}ft \\ =1070.89acre-feet \end{gathered}$$

Rounding off to correct significant figures, volume of water in is$1.1\times {10}^{3}acrefeet$.