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Dupuit Method

This document contains calculations for modeling flow through a dam using several methods. It provides dimensions for an actual dam with an upstream water depth of 50 feet, downstream depth of 0 feet, dam height of 55 feet, and crest width of 20 feet. It then models flow through the dam using the Dupuit, Casagrande, Pavlovsky, and blanket drain methods and outputs values for flow rate and water depth at intervals along the dam.

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Mahmoud I. Mahmoud
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75 views3 pages

Dupuit Method

This document contains calculations for modeling flow through a dam using several methods. It provides dimensions for an actual dam with an upstream water depth of 50 feet, downstream depth of 0 feet, dam height of 55 feet, and crest width of 20 feet. It then models flow through the dam using the Dupuit, Casagrande, Pavlovsky, and blanket drain methods and outputs values for flow rate and water depth at intervals along the dam.

Uploaded by

Mahmoud I. Mahmoud
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
Available Formats
Download as XLS, PDF, TXT or read online on Scribd
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Solutions to Dam Flow Problems Name:

Date: 7/15/2020

Kx = 0.002 ft/min Kx/Ky = 3.0


Kz = 0.00022222 ft/min SQRT(KxKy 0.00066667 Dupuit Dupuit(0.3D) Casagrande Pavlovsky Blanket

Actual Dimensions Transform Dimensions q= 5.952E-3 4.902E-3 7.130E-3 4.433E-3 2.123E-02


~~~~~~~~~~~~~~~~~ ~~~~~~~~~~~~~~~~~~~~ a= -- -- 53.5 29.7 47.8
** DeltaX = 8.0 Feet DeltaX = 8.0 Feet Upstream Length under Water = 100.0 Feet ao = 23.9 13.3
Upstream Water Dpth= 50.0 Feet Upstream Water Dpth= 150.0 Feet Total Upstream Length = 110.0 Feet
Downstream Water Dpth 0.0 Feet Downstream Water Dpth 0.0 Feet Total Downstream Length = 110.0 Feet
Crest Wdth 20.0 Feet Crest Wdth 20.0 Feet Total Length of Dam = 240.0 Feet
Dam Height 55.0 Feet Dam Height 165.0 Feet
UpStrm Slope = 2.0 :1 (Hor:Vert) 0.46365 UpStrm Slop 0.6667 :1 (Hor:Vert) alpha = 0.983
DownStrm = 2.0 :1 (Hor:Vert) 0.46365 DownStrm 0.6667 :1 (Hor:Vert) beta = 0.9828
Delta = 30.0
** DeltaX is the spacing between calculated points.
Remember to page down to Variables for Pavlovsky, Blanket Drain and Height of Graph.

Dupuit Method
~~~~~~~~~~~~~ Ho^2 = 22500.0 (Ho^2 - H1^2) = 22500.0

------> At Water Line: d= 140.0


x= 0.0 8.0 16.0 24.0 32.0 40.0 48.0 56.0 64.0 72.0 80.0 88.0 96.0 104.0 112.0 120.0 128.0 136.0 140.0 140.0 140.0
H= 150.0 145.7 141.2 136.5 131.7 126.8 121.6 116.2 110.5 104.5 98.2 91.4 84.1 76.1 67.1 56.7 43.9 25.4 0.4 0.4 0.4
H-actual = 50.0 48.6 47.1 45.5 43.9 42.3 40.5 38.7 36.8 34.8 32.7 30.5 28.0 25.4 22.4 18.9 14.6 8.5 0.1 0.1 0.1
x'= 100.0 108.0 116.0 124.0 132.0 140.0 148.0 156.0 164.0 172.0 180.0 188.0 196.0 204.0 212.0 220.0 228.0 236.0 240.0 240.0 240.0
qbar = 5.952E-3 ft^3/min change = 10.0

------> At 0.3*Delta: d= 170.0


x= 0.0 8.0 16.0 24.0 32.0 40.0 48.0 56.0 64.0 72.0 80.0 88.0 96.0 104.0 112.0 120.0 128.0 136.0 144.0 152.0 160.0
H= 150.0 146.4 142.8 139.0 135.1 131.2 127.1 122.8 118.4 113.9 109.1 104.2 99.0 93.5 87.6 81.3 74.6 67.1 58.7 48.8 36.4
H-actual = 50.0 48.8 47.6 46.3 45.0 43.7 42.4 40.9 39.5 38.0 36.4 34.7 33.0 31.2 29.2 27.1 24.9 22.4 19.6 16.3 12.1
x'= 70.0 78.0 86.0 94.0 102.0 110.0 118.0 126.0 134.0 142.0 150.0 158.0 166.0 174.0 182.0 190.0 198.0 206.0 214.0 222.0 230.0
qbar = 4.902E-3 ft^3/min change = 40.0

Casagrande Method
~~~~~~~~~~~~~~~~~
d= 170.0 a' = 23.9 Ho^2-a'^2= 17352.6
S1 = 226.7 S2 = 231.6
a1 = 89.2 a2 = 86.2 d-a2cos()= 122.2 L= 47.8 a= 53.5

x= 0.0 8.0 16.0 24.0 32.0 40.0 48.0 56.0 64.0 72.0 80.0 88.0 96.0 104.0 112.0 120.0 122.2 122.2 122.2 122.2 122.2
H= 150.0 146.2 142.2 138.2 134.0 129.7 125.2 120.6 115.8 110.8 105.5 100.0 94.2 87.9 81.2 73.9 71.7 71.7 71.7 71.7 71.7
H-actual = 50.0 48.7 47.4 46.1 44.7 43.2 41.7 40.2 38.6 36.9 35.2 33.3 31.4 29.3 27.1 24.6 23.9 23.9 23.9 23.9 23.9
x'= 70.0 78.0 86.0 94.0 102.0 110.0 118.0 126.0 134.0 142.0 150.0 158.0 166.0 174.0 182.0 190.0 192.2 192.2 192.2 192.2 192.2
qbar = 7.130E-3 change = 40.0

Pavlovsky's Method
~~~~~~~~~~~~~~~~~~
Guess --> h= 118.5 h-actual= 39.5 b/cot()+Hd = 195.0
Compare--> a1 = 40.1 a1-actual= 13.4 h^2 = 14042.3
and-----> a2 = 39.9 a2-actual= 13.3 d= 103.4
h^2-a2^2= 12450.7

x= a2 = 8.0 16.0 24.0 32.0 40.0 48.0 56.0 64.0 72.0 80.0 88.0 96.0 103.4 103.4 103.4 103.4 103.4 103.4 103.4 103.4
H= #VALUE! 114.4 110.1 105.6 100.9 96.1 90.9 85.4 79.6 73.3 66.4 58.7 49.8 39.9 39.9 39.9 39.9 39.9 39.9 39.9 39.9
H-actual = #VALUE! 38.1 36.7 35.2 33.6 32.0 30.3 28.5 26.5 24.4 22.1 19.6 16.6 13.3 13.3 13.3 13.3 13.3 13.3 13.3 13.3
x' = 110.0 118.0 126.0 134.0 142.0 150.0 158.0 166.0 174.0 182.0 190.0 198.0 206.0 213.4 213.4 213.4 213.4 213.4 213.4 213.4 213.4
qbar = 4.433E-3

Blanket Drain
~~~~~~~~~~~~~
Length of Drain = 100.0 yo = 95.5 Start Drain = 140.0
d= 70.0 a= 47.8 Length = d + a = 117.8 x adjust 70.0

x = -70.0 -62.0 -54.0 -46.0 -38.0 -30.0 -22.0 -14.0 -6.0 2.0 10.0 18.0 26.0 34.0 42.0 47.8 47.8 47.8 47.8 47.8 47.8
h= 150.0 144.8 139.4 133.8 128.0 121.9 115.5 108.6 101.4 93.5 84.9 75.4 64.5 51.3 33.2 0.0 0.0 0.0 0.0 0.0 0.0
h-actual = 50.0 48.3 46.5 44.6 42.7 40.6 38.5 36.2 33.8 31.2 28.3 25.1 21.5 17.1 11.1 0.0 0.0 0.0 0.0 0.0 0.0
x' = 70.0 78.0 86.0 94.0 102.0 110.0 118.0 126.0 134.0 142.0 150.0 158.0 166.0 174.0 182.0 187.8 187.8 187.8 187.8 187.8 187.8
qbar = 2.123E-02

Dam Outline:
X= 0 110.0 130.00 240.00
Y= 0 55.0 55.0 0
Y'= 0 165.0 165.0 0
Upstream Water:
X= 0 100.0
Y= 50.0 50.0
Y'= 150.0 150.0
Adjust Height of Plot
X= 0 0
Y= 0 260
Y'= 0 260
Blanket
X= 240.0 140.0
Y= 0 0

Page -
Flow Through Dam

300.0

Dam
Upstream Water
250.0 Dupuit from Water Surface
Dupuit from 0.3Delta
Casagrande
Pavlosky
200.0 Adjust Height
Blanket Drain
Blanket

150.0
Y (ft)

100.0

50.0

0.0
0.0 50.0 100.0 150.0 200.0 250.0 300.0

X (ft)
Flow Through Transformed Dam

300.0

Dam
Upstream Water
250.0 Dupuit from Water Surface
Dupuit from 0.3Delta
Casagrande
Pavlosky
200.0 Adjust Height
Blanket Drain
Blanket

150.0
x(ft)

100.0

50.0

0.0
0.0 50.0 100.0 150.0 200.0 250.0 300.0

Y (ft)

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