CE 4603: Water Resources Engineering
====== Homework #3 Due 2/9 ======
//Solve problems 5.2, 5.6, 5.11, 5.140, and 5.15 of Water Resources Engineering by David Chin, 2<sup>nd</sup> edition, ages 585-587.  Hint: Problem 5.6, for Atlanta, using Fig. 5.5-5.7 you should get 
R<sup>10</sup><sub>1</sub>=2.7 in.,
R<sup>10</sup><sub>24</sub>=5.7 in.,
R<sup>100</sup><sub>1</sub>=3.75 in.//

====== 5.2 ======
n=	50					
T<sub>R</sub> = (n+1)/m

^Rank (m)	^Return (yr)^	5 ^	10 ^	15 ^	20 ^	25 ^	30 ^
^1	^51|	26.2|	45.8|	60.5|	72.4|	81.8|	89.7|
^//(Interpoloated)//^	//40.0//|	//25.8//|	//45.0//|	//59.5//|	//71.2//|	//80.4//|	//88.2//|
^2	^25.5|	25.3|	44.0|	58.1|	69.6|	78.6|	86.3|
^3	^17|	24.2|	42.2|	55.8|	66.8|	75.5|	82.8|

{{hw_3_5-2.jpg}}

^	Duration (min)^	5	^ 10	^ 15	^ 20	^  25	^  30 ^
^	Intensity (mm/hr)|	309.74|	270.14|	237.86|	213.58|	193.01|	176.47|

====== 5.6 ======
x=R10,1/R10,24=	47%					
a1=	28.3					
b1=	9.1					
c1=	0.79					
Tp=	9.49					
a=	77.32	

{{hw_3_5-6.jpg}}

^  Duration (min)^	5^	10^	15^	20^	25^	30^
^  Intensity (in/hr)|	9.56|	7.52|	6.26|	5.39|	4.76|	4.27|

i = a/(t+b<sub>1</sub><sup>c1</sup>)






====== 5.11 ======
{{   hw_3_5-11.jpg?200}}
t<sub>d</sub> = 50 min = 50/60 hr

i = 818/(t<sub>d</sub> + 8.54)<sup>0.76</sup>)
 = 818/(50 + 8.54)<sup>0.76</sup>) = 37.18 mm/hr

P<sub>50</sub> = 37.18 mm/hr * 50/60 = 31mm

t<sub>p</sub>/t<sub>d</sub> = 3 t<sup>bar</sup> / t<sub>p</sub> -1 = 3 x 0.44 - 1 = 0.32
-> t<sub>p</sub> = t<sub>d</sub> x 0.32 = 50/60 x 0.32 = 0.267 hr = t<sub>p</sub>

½i<sub>p</sub>t<sub>d</sub> = 37.18 -> i<sub>p</sub> = 37.18/(½t<sub>d</sub>) =  2 x 37.18/ (50/60) = 89 mm/hr = i<sub>p</sub>







====== 5.14 ======
a=64.1
b<sub>1</sub>=8.16
c<sub>1</sub>=0.76
T=10
t=50 min = 50/60 hr
Δt=50/7
i=a/(t+b<sub>1</sub>)<sup>c1</sup>=64.1/(nΔt+8.16)<sup>0.76</sup>

{{hw_3_5-14.jpg}}

^Increment	^//T (min)//	^I (mm/hr)	^It (mm)	^Rainfall (mm)	^Intensity (mm/hr)	^//Ordered//^
|1|	//7.14//|	8.06|	0.96|	0.96|	8.06|	//0.16//|
|2|	//14.29//|	6.03|	1.43|	0.47|	1.99|	//0.31//|
|3|	//21.43//|	4.88|	1.74|	0.31|	0.87|	//0.87//|
|4|	//28.57//|	4.14|	1.97|	0.23|	0.48|	//8.06//|
|5|	//35.71//|	3.62|	2.16|	0.18|	0.31|	//1.99//|
|6|	//42.86//|	3.23|	2.31|	0.15|	0.21|	//0.48//|
|7|	//50//|	2.92|	2.44|	0.13|	0.16|	//0.21//|

//Please note the text does not specify whether the values for the empirical formula for i yields mm/hr as assumed here, or in/hr.//


====== 5.15 ======



Storms dumping the same amount of rain in a shorter period of time would be even more intense, and hence less frequent.  Assuming the same return period will tend to overestimate the frequency of these shorter-duration storms and is therefore a conservative estimate.