b The figure shows the cross section of a channel carrying water. Determine h, b and that minimize the length of the wetted perimeter while maintaining a cross- sectional area of 8 m². (Minimizing the wetted perimeter results in least resistance to the flow.) Ans: 14- Given. A = 8m² To Find: ktb h A Determine, h, b, 0 of wetted perimeter. h tano = m that minimize the length

Operations Research : Applications and Algorithms
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ISBN:9780534380588
Author:Wayne L. Winston
Publisher:Wayne L. Winston
Chapter11: Nonlinear Programming
Section11.2: Introductory Concepts
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b
The figure shows the cross section of a channel carrying water. Determine h, b
and that minimize the length of the wetted perimeter while maintaining a cross-
sectional area of 8 m². (Minimizing the wetted perimeter results in least resistance to
the flow.)
Ans:
14-
KH
h
b
tant = m
Given.
A = 8m²
To Find:
Determine, h, b, 0 that minimize the length
of wetted perimeter.
Transcribed Image Text:b The figure shows the cross section of a channel carrying water. Determine h, b and that minimize the length of the wetted perimeter while maintaining a cross- sectional area of 8 m². (Minimizing the wetted perimeter results in least resistance to the flow.) Ans: 14- KH h b tant = m Given. A = 8m² To Find: Determine, h, b, 0 that minimize the length of wetted perimeter.
As we
(1)
(ül)
A = √3
know, Face minimum perimeter (P)
2
= √3h²
(li) b = 2h
√3
y²
2
8 = √3 6²² + h = 2.15m.
And
b
tano =
T = 2 b
2=
tan o =
tano
2.48m.
=
2x2.15
53
(T-b)
h
(2b-b)
h
b
2h
0 = 29.97°
B
tan (25) =
tan
(b/₂).
h
2.48
2 X2.15
Transcribed Image Text:As we (1) (ül) A = √3 know, Face minimum perimeter (P) 2 = √3h² (li) b = 2h √3 y² 2 8 = √3 6²² + h = 2.15m. And b tano = T = 2 b 2= tan o = tano 2.48m. = 2x2.15 53 (T-b) h (2b-b) h b 2h 0 = 29.97° B tan (25) = tan (b/₂). h 2.48 2 X2.15
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