Hydrology: additional unit conversion problems …

1 hydrology : additional unit conversion problems ( solutions ) 1. You measure a distance of stream channel on a 1:50,000 scale topographic map. What is the actual distance of that stream reach in miles? Known information: inches map distance Scale: 1 inch (map distance) = 50,000 inches (ground distance) Conversions: 12 inches = 1 foot 5,280 feet = 1 mile Solution: ( in map distance) (50,000 in ground distance / 1 in map distance) (1 ft / 12 in) (1 mi / 5,280 ft) = miles 2. A rectangular parcel measures x inches on a 1:24,000 topographic map. What is the size of that parcel in square miles? Known information: x inches map distance Scale: 1 inch (map distance) = 24,000 inches (ground distance) Conversions: 12 inches = 1 foot 5,280 feet = 1 mile Solution: Convert linear map distances to miles of ground distance, then multiply: ( in map distance) (24,000 in ground distance / 1 in map distance) (1 ft / 12 in) (1 mi / 5280 ft) = miles ( in map distance) (24,000 in ground distance / 1 in map distance) (1 ft / 12 in) (1 mi / 5280 ft) = miles Area = ( mi) ( mi) = mi2 Note: Do not apply the map scale for distance (1: 24,000) to area units.

2 To do so, you need to square the scale: Map scale in area units = (1)2 in2 map area = (24,000) 2 in2 ground area 1 in2 map area = 576,000,000 in2 ground area 3. A storm delivers inches of rain over a 100 acre residential watershed. If 60% of the rain runs off, how many gallons of water infiltrated the soil? Known information: inches rain 100 acre area Conversions: 12 inches = 1 foot 43,560 ft2 = 1 acre 1 ft3 = gal Solution: Calculate volume of rain (Note: depth (ft) X area (ft2) = volume (ft3)): ( in) (1 ft / 12 in) (100 ac) (43,560 ft2) = 907,500 ft3 Multiply by 40% ( ) to determine volume that infiltrated (100% - 60% runoff): (907,500 ft3) ( ) = 363,000 ft3 Convert to gallons: (363,000 ft3) ( gal / 1 ft3) = 2,715, gal