Design of Swales 2 Norman W. Garrick CE 4410 Spring 2017 Lecture 17

Calculations for Trapezoidal Swale Calculate the a) flow velocity , b) flow volume for the trapezoidal vegetative swale shown. The slope of the channel is 2% and the Manning’s roughness coefficient is 0.10. 2.438 m 1.219 m 0.6095 m 1.362 m

Calculations for Trapezoidal Swale Calculate the flow velocity V = (R2/3 S1/2)/n >>>>>>> note… metric… do not include 1.48 R = Area/Wetted Perimeter A = (2.438+1.219)*0.6095 = 2.2289 m2 WP = 1.362+2.438+1.362 = 5.162 m R = 5.162/2.2289 = 2.3159 m 2.438 m 1.219 m 0.6095 m 1.362 m

Calculations for Trapezoidal Swale Calculate the flow velocity V = (R2/3 S1/2)/n R = 2.3159 m S = 0.02 n = 0.10 V = 2.31590.666*0.020.5/0.10 Velocity = 0.81 m/s2 2.438 m 1.219 m 0.6095 m 1.362 m

Calculations for Trapezoidal Swale Calculate the flow volume q = AV = 2.2289 * 0.81 Flow Volume = 1.81 cu. m./s 2.438 m 1.219 m 0.6095 m 1.362 m

Designing Parabolic Swales Using Charts

Retardance for Parabolic Swale Each chart is based on a RETARDANCE value The retardance varies with the type of grass, how good the stand is, and the height of the grass Retardance A provides the most resistance to flow Retardance E the least resistance to flow

Retardance A Weeping Lovegrass 30 in

Retardance B Bermuda Grass 12 in

Retardance E Bermuda Grass 1.5 in

Swale Design with Chart Design a swale that will have a good stand of Kentucky bluegrass that will be mowed to stay between 2 and 10 inches tall. The soil is easily eroded and the grade of the swale is 5% This swale should be designed to carry 36 cubic feet per second of water.

Swale Design with Chart We need to design so that Permissible Velocity is not exceeded We have enough capacity

Swale Design with Chart What is the critical condition for PERMISSIBLE VELOCITY? Good stand Kentucky Blue Grass, 2 inches high Good stand Kentucky Blue Grass, 10 inches high What is the critical condition for CAPACITY?

Swale Design with Chart PERMISSIBLE VELOCITY Good stand Kentucky Blue Grass, 2 inches high Permissible velocity = 4 ft/s ….. Table 13.1 Retardance for 2 inch high Kentucky Blue Grass is Retardance D Need A, W, D for design

Swale Design with Chart PERMISSIBLE VELOCITY Need A, W, D for design q = AV 36 = A*4 >>>>> A = 9 ft2 Get R from Chart Figure 13.9(d) R = 0.43

Swale Design with Chart PERMISSIBLE VELOCITY R = 0.43 ft, A = 9 ft2 Try, D = 1.5 R D = 1.5*0.43 = 0.65 ft Parabolic Swale Hydraulic Radius = Cross-section Area/Wetted Perimeter Hydraulic Radius: R = W2D/(1.5W2+4D2) Area: A = 2/3 WD

Swale Design with Chart PERMISSIBLE VELOCITY Substitute for D = 0.65 into A = 2/3 WD 9 = 2/3 W*0.65 W = 20.8 ft

Swale Design with Chart When the grass is 2 inches high W = 20.8 ft and D = 0.65 ft is ok What happens when grass is 10 inch high? Flow velocity slows down Area needed for carrying the peak run-off increases W1 = 20.8 ft D1 = 0.65 ft

Swale Design with Chart Do we have enough capacity for high grass situation? When grass is 10 inch high Retardance is C We need larger D Assume D = 0.75 ft D2 = ?

Swale Design with Chart Assume D = 0.75 ft Again take R = 1.5 D >>>>> D = R/1.5 = 0.5 ft From Figure 13.9c V = 3.4 ft2/s D2 = ?

Swale Design with Chart V = 3.4 ft2/s Is D = 0.75 adequate for q = 36 cubic feet/second q = AV D2 = ?

Swale Design with Chart To get A we need to calculate W2 W2 = W1 (D2/D1)0.5 = 20.8(0.75/0.65)0.5 = 22.3 ft A = 2/3 WD = 11.15 ft2 W2 = ? D2 = 0.75

Swale Design with Chart q = AV = 11.15*3.4 = 37.91 cubic feet/s Adequate capacity W2 = 22.3 ft D2 = 0.75