From the annual series information given in Problem 1, find the relation between the mean annual flow and drainage area. (Note that the functional expression should be of the form Q2.33 = rAs.)
Problem 1
Use the following data to determine a best-fit relationship in the form of Eq. 8.7 between the drainage area and 50-yr flood for the given region.
Peak Flood Frequency Discharges (cfs) for Stations in the Rappahannock River Basin | |||||||
Station | Drainage area (mi) | Type of series | 2.33 (mean) | Return period in years | |||
5 | 10 | 25 | 50 | ||||
Rappahannock |
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River near | 192 | Annual | 4,150 | 8,350 | 9,000 | 14,000 | 19,250 |
Warrenton, VA |
| Partial | 4,600 | 8,650 | 9,200 | 14,000 | 19,250 |
Rush River at |
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Washington, VA | 15.2 | Annual | 530 | 860 | 1,290 | 2,100 | 3,000 |
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| Partial | 610 | 900 | 1,310 | 2,100 | 3,000 |
Thornton River |
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near Laurel | 142 | Annual | 5,900 | 11,500 | 19,900 | 34,000 | 48,000 |
Mills, VA |
| Partial | 7,200 | 12,500 | 20,500 | 34,000 | 48,000 |
Hazel River at | 286 | Annual | 7,300 | 11,800 | 17,200 | 25,000 | 41,000 |
Rixeyville, VA |
| Partial | 8,300 | 12,400 | 18,000 | 25,500 | 41,000 |
Rappahannock |
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River at | 616 | Annual | 11,000 | 14,500 | 18,100 | 24,500 | 31,000 |
Remington, VA |
| Partial | 12,000 | 15,200 | 18,900 | 25,000 | 31,000 |
Rappahannock |
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River at Kellys | 641 | Annual | 12,300 | 19,000 | 26,800 | 42,000 | 57,500 |
Ford, VA |
| Partial | 14,000 | 20,000 | 27,500 | 42,000 | 57,500 |
Mountain Run near | 14.7 | Annual | 750 | 1,750 | 3,350 | 6,000 | 10,000 |
Culpeper, VA |
| Partial | 950 | 1,900 | 3,550 | 6,000 | 10,000 |
Rapidan River near | 111 | Annual | 3,950 | 7,100 | 11,600 | 21,000 | 34,000 |
Ruckersville , VA |
| Partial | 4,700 | 7,700 | 12,000 | 21,000 | 34,000 |
Robinson River near | 180 | Annual | 4,600 | 7,000 | 9,800 | 15,400 | 21,500 |
Locust Dale, VA |
| Partial | 5,150 | 7,300 | 10,100 | 15,800 | 21,500 |
Rapidan River near | 456 | Annual | 9,100 | 16,400 | 26,900 | 50,000 | 78,000 |
Culpeper, VA |
| Partial | 10,800 | 17,600 | 27,600 | 50,000 | 78,000 |
Rappahannock |
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River near |
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Fredericksburg, VA | 1,599 | Annual | 26,000 | 39,900 | 55,000 | 85,000 | 117,000 |
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| Partial | 29,300 | 42,000 | 57,500 | 85,000 | 117,000 |
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