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STALIN [3.7K]
3 years ago
6

A soil has the following Green-Ampt parameters Effective porosity 0.400 Initial volumetric moisture content-15% Hydraulic Conduc

tivity-0.10 cm/hr Capillary suction 20 cm If a constant intensity rainfall of 1.0 cm/hr falls for 5 hours, model the infiltration rate (f) and cumulative infiltration (F) as a function of time for the entire storm. Use 0.25 hour time increment. Include the following items in your solution [35 points]: a. A graph of infiltration rate vs. time for zero to five hours b. A graph of cumulative infiltration vs. time for zero to five hours c. A table that includes all values used to plot the above two graphs. d. Detailed sample calculations for the first time step after ponding.

Engineering
1 answer:
Rudik [331]3 years ago
5 0

Answer:

The graphs are attached below

Explanation:

Ans) We know,

F(t) = K(t - to) + zΔ∅ ln[(1 + F(t)/zΔ∅]

where K = hydraulic conductivity =0.1 cm/hr

z = capillary suction =20cm

 Δ∅ = ∅ (1 - Se)

 ∅ = effective porosity , Se = initial moisture content

 Δ∅ = 0.40(1 - 0.15)

Δ∅ = 0.34

Now, F(t) = 0.1(t - to) + 20(0.34) ln[ 1 + F(t)/6.8]

F(t) = 0.1(t - to) + 6.8 ln [1+ 0.147 F(t)]

Also, infiltration rate (f),

f = K [(zΔ∅ + F)/F]

f = 0.40 [6.8 + F]/F

Condition of ponding,

Ponding time tp = K zΔ∅ i(i-k)

where, i = rainfall rate (1cm/hr)

tp = 0.40(6.8) / 0.60

tp= 4.53 hours

Now, cumulative infiltraton at ponding Fp = i tp

Fp = 1 x 4.53 or 4.53 cm

For infiltration at time less then ponding time , infiltration rate = rainfall rate

For t = 0.25 hr , f = 1cm/hr ; F = 0.25 x 1 = 0.25 cm

For t = 0.50 hr , f = 1cm/hr ; F = 0.50 cm

For t = 0.75 hr , f = 1cm/hr ; F = 0.75 cm

For t = 1 hr , f = 1cm/hr ; F = 1cm/hr

For t > tp ,

Equivalent time origin(to),

to = tp - 1/K [ Fp - z Δ∅ ln (1+ Fp/zΔ∅)

to = 4.53 - 1/0.40[ 4.53 - 6.8 ln(1 + 0.66)

to = 4.53 - 2.5 ( 4.53 - 3.44)

to = 1.82 hr

Hence,

F = 0.10( t - 1.82) + 6.8 ln[ 1+ 0.147F(t)]

Solving above equation for t by assuming F, and further solving equation for infiltration rate

Ans (a) Following is required curve :

O.S 1-5 2 time Chr)ホー Lt 2 time Chr)

Ans (c) Following is required table :

Ans (d) For time step t = 0.25 hrs

At t < tp ; i = f = 1 cm/hr

F = i x t

F = 1 x 0.25

F = 0.25 cm  

 

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Explanation:

Solution:

Note: This question is incomplete and lacks necessary data to solve. But I have found the similar question on the internet. So, I will be using the data from that question to solve this question for the sack of concept and understanding.

Data Given:

x = 27 , 44 , 32 , 47, 23 , 40, 34, 52

y = 30, 19,  24,  13 , 29,  19,  21,  14

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We are asked to verify the above values manually in this question.

So,

1. ∑x = 299

Let's verify it:

∑x = 27 + 44 + 32 + 47 + 23 + 40 + 34 + 52

∑x = 299

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2. ∑y = 167

Let's verify it:

∑y = 30 + 19 +  24 + 13 + 29 + 19 +  21 +  14

∑y = 169

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3. ∑x^{2} = 11887

Let's verify it:

For this to find,  first we need to square all the value of x individually and then add them together to verify.

∑x^{2} = 27^{2} + 44^{2} + 32^{2} + 47^{2} + 23^{2} + 40^{2} + 34^{2} + 52^{2}

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Yes, it is equal to the given value. Hence, verified.

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Let's verify it:

Again, for this we need to find the squares of all the y values and then add them together to verify it.

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