Q7p - Fundamentals Of Physics

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?

Step-by-Step Solution

Answer

 

Answer

 

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

Step 1: Given data

Thunderstorm dumped 2.0 in. of rain in 30 min.

Area of town is 26km² .

 

Step 2: 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.

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

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

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

 

Now, convert the area from into acre

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

 

Thus, the area is $6425.39 acre$.

 

Step 4: conversion of height in ft.

The height of the rainfall is,h= 2.0 inch 

 

Now, convert height from inch to ft.

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

 

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

Step 5: Determination of volume of water

Volume of water fall is calculated as: 

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

 

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