Question

Using the worksheet, calculate a Tc or Tt for the basins:

1. 1) Jefferson County, Arkansas

   1. AB sheet flow 85 lf, Bermuda grass, slope is 2%

   2. BC shallow concentrated flow 300 lf, short grass prairie, slope 4%

   3. CD channel flow 1200 lf, dirt ditch 6’x6’, 90 degree sides, 4’ deep flow, slope 2%

2. 2) Gordon County, Georgia

   1. AB sheet flow 100 lf, short grass prairie grass, slope is 1%

   2. BC shallow concentrated flow 600 lf, Bermuda & brush, slope 4%

   3. CD channel flow 2500 lf, concrete ditch 10’x10’, 90 degree sides, 4’ deep flow,

slope 2%
Please note the source of any values that you research.

Answer 1

Ans 1) We know, time of concentration (t_{c ,AB}) for sheet flow :

t_{c, AB} = 0.007 (NL)^0.8 / P^0.5 S^0.4

where, N = Manning roughness coefficient = 0.41 for bermuda grass

L = Sheet flow length = 85 ft

   P = 2 yr 24 rainfall = 2.4 in for Jefferson, Arkansas (from NRCS data)

S = Slope = 2%

Putting values,

t_c = 0.007 (0.41 x 85)^0.8 / (2.4)^0.5 (0.02)^0.4

  => t_c = 0.37 hr or 22.2 min

Now,

For shallow concentrated flow , t_{c, BC} = Length / Velocity

Velocity of flow for short grass prairie = 6.962 s^1/2

=> V = 6.962 (0.04)^1/2 = 1.39 ft/s

=> t_c,BC = 300 ft / 1.39 ft/s

=> t_c,BC = 215.8 sec or 3.60 min

Now,

For channel flow flow , t_c,CD = Length / Velocity

Velocity of flow for channel flow = (1/N) R^2/3 S^1/2

where, N = Manning roughness coefficient = 0.025 for dirt ditch

   R = Hydraulic depth = Area / Wetted perimeter

Area = 6 x 6 = 36 ft²

Wetted perimeter = B + 2 D = 6 + 2(4) = 14 ft

=> R = 36 / 14 = 2.57 ft

=> V = (1 / 0.025) (2.57)^2/3 (0.02)^1/2

=> V = 10.61 ft/s

=> t_c,CD = 1200 / 10.61 = 113.1 sec or 1.88 min

Total time of concentration = t_c,AB + t_c,BC + t_c,CD = 22.2 + 3.6 + 1.88 = 27.68 min

Ans 2) We know, time of concentration (t_{c ,AB}) for sheet flow :

t_{c, AB} = 0.007 (NL)^0.8 / P^0.5 S^0.4

where, N = Manning roughness coefficient = 0.15 for short grass prairie

L = Sheet flow length = 100 ft

   P = 2 yr 24 rainfall = 2 in for Jefferson, Arkansas (from NRCS data)

S = Slope = 1%

Putting values,

t_c = 0.007 (0.15 x 100)^0.8 / (2)^0.5 (0.01)^0.4

  => t_c = 0.27 hr or 16.2 min

Now,

For shallow concentrated flow , t_{c, BC} = Length / Velocity

Velocity of flow for long grass = 2.516 s^1/2

=> V = 2.516 (0.04)^1/2 = 0.5 ft/s

=> t_c,BC = 600 ft / 0.5 ft/s

=> t_c,BC = 1200 sec or 20 min

Now,

For channel flow flow , t_c,CD = Length / Velocity

Velocity of flow for channel flow = (1/N) R^2/3 S^1/2

where, N = Manning roughness coefficient = 0.012 for concrete ditch

   R = Hydraulic depth = Area / Wetted perimeter

Area = 10 x 10 = 100 ft²

Wetted perimeter = B + 2 D = 10 + 2(4) = 18 ft

=> R = 100 / 18 = 5.55 ft

=> V = (1 / 0.012) (5.55)^2/3 (0.02)^1/2

=> V = 37 ft/s

=> t_c,CD = 2500 / 37 = 67.56 sec or 1.12 min

Total time of concentration = t_c,AB + t_c,BC + t_c,CD = 16.2 + 20 + 1.12 = 37.32 min