Subido por Erick Vargas Flores

SOLUCIONARIO PRÁCTICA Nº1 - CIV 230 - 2-2022

Anuncio
UNIVERSIDAD AUTÓNOMA "TOMÁS FRÍAS"
FACULTAD DE INGENIERÍA
CARRERA DE INGENIERÍA CIVIL
HIDRÁULICA II Y LABORATORIO - CIV 230
SOLUCIONARIO PRÁCTICA Nº1
ELEMENTOS GEÓMETRICOS DE SECCIONES DE
CANALES ABIERTOS
EJERCICIO. – Establecer las características geométricas de las secciones mostradas en las
figuras:
a) Área de la sección transversal (A)
b) Perímetro Mojado (P)
c) Espejo de Agua ó Superficie Libre del agua (B)
d) Radio Hidráulico (RH)
e) Profundidad de flujo (y), en las secciones donde se tenga un ángulo (θ)
FIGURA Nº1
Del gráfico tenemos:
A = A1 + 2 A2 + 2 ⋅ A3 - 2 ⋅ A4
⎛D D⎞ ⎛ D D⎞
D2
A1 = ⎜―+ ―⎟ ⋅ ⎜2 ⋅ ―+ ―⎟ → A1 = ――
4⎠ ⎝ 4
2⎠
2
⎝4
θ ⋅ D2
D2
1 ⎛D ⎞ D
1 ⎛D⎞ ⎛D⎞
A2 = ―⋅ ⎜―⋅ θ⎟ ⋅ ―→ A2 = ―― ; A4 = ―⋅ ⎜―⎟ ⋅ ⎜―⎟ → A4 = ――
2 ⎝2 ⎠ 2
2 ⎝4⎠ ⎝4⎠
8
32
1 D
D
A3 = ―⋅ ―⋅ sin (θ) ⋅ ―⋅ cos (θ)
2 2
2
Espejo de Agua:
D
B = 2 ⋅ ―⋅ cos (θ)
2
Perímetro:
⎛
⎛ D ⎞⎞
D
D
D
2 ⋅ ⎜―⎟⎟ + 2 ⋅ ―+ 2 ⋅ ―⋅ θ
P = ―+ 2 ⎜ ‾‾
2
4
2
⎝
⎝ 4 ⎠⎠
Radio Hidráulico:
=>
=>
D2
θ ⋅ D2
D2
D2
+ 2 ―― + 2 ⋅ ――
⋅ sin (2 θ) - 2 ⋅ ――
A = ――
2
8
16
32
=>
D 2 ⎛ sin (2 ⋅ θ)
7⎞
⋅ ⎜―――+ θ + ―
A = ――
⎟
2
4⎠
4 ⎝
=>
=>
⎛
⎞
‾‾
2⎟
P = D ⋅ ⎜θ + 1 + ――
⎜⎝
2 ⎟⎠
⎛ sin (2 ⋅ θ) 7
⎞
D ⋅ ⎜―――+ ―+ θ⎟
2
4
⎝
⎠
Rh = ―――――――
⎛ ‾‾
⎞
2
4 ⋅ ⎜――
+ θ + 1⎟
⎜⎝ 2
⎟⎠
D D
D
y = ―+ ―⋅ sin (θ) = ―⋅ (1 + sin (θ))
2
2
2
AUX: UNIV. GABRIEL ALZU SOLA
D2
⋅ sin (2 θ)
A3 = ――
16
B = D ⋅ cos (θ)
D 2 ⎛ sin (2 ⋅ θ)
7⎞
⋅ ⎜―――+ θ + ―
――
⎟
2
4⎠
4 ⎝
Rh = ――――――――
⎛
⎞
‾‾
2⎟
D ⋅ ⎜θ + 1 + ――
2 ⎠⎟
⎝⎜
Profundidad del Flujo:
=>
=>
D
y = ―⋅ (1 + sin (θ))
2
SEMESTRE II/2022
UNIVERSIDAD AUTÓNOMA "TOMÁS FRÍAS"
FACULTAD DE INGENIERÍA
CARRERA DE INGENIERÍA CIVIL
HIDRÁULICA II Y LABORATORIO - CIV 230
FIGURA Nº2
Del gráfico tenemos:
⎛π⎞
3
L ⋅ ‾‾
p = L ⋅ sin ⎜―
⎟ → p = ―――
2
⎝3⎠
π
60 ° = ―
3
2 ⋅ ‾‾
3 ⋅ (y - p)
y-p
q = ―――
→ q = ―――――
⎛π⎞
3
sin ⎜―
⎟
⎝3⎠
Área:
(y - p) ⋅ ‾‾
3
y-p
x = ―――
→ x = ――――
⎛π⎞
3
tan ⎜―
⎟
⎝3⎠
A = A1 + A2 = 3 ⋅ A4 + A2
1
A4 = ―⋅ L ⋅ p
2
=>
3
3
L 2 ⋅ ‾‾
1
L ⋅ ‾‾
A4 = ―⋅ L ⋅ ―――
→ A4 = ―――
2
4
2
(y - p)
B=2 L - 2 ⋅ x
A2 = (2 ⋅ L + B) ⋅ ―――;
2
⎛
⎞
3 ⎟ (y - p)
(y - p) ⋅ ‾‾
A2 = ⎜2 ⋅ L + 2 L - 2 ⋅ ――――
⋅ ―――
⎜⎝
⎟⎠
3
2
2
=>
2
‾‾
3 (
A2 = 2 ⋅ L ⋅ (y - p) - ――
⋅ y - p)
3
=>
ó:
Perímetro:
P=3 L + 2 q
Espejo de Agua:
Radio Hidráulico:
=>
⎛
⎞
⎛
⎞
‾‾
3
3⎟
3 ⎜
3⎟
L 2 ⋅ ‾‾
L ⋅ ‾‾
L ⋅ ‾‾
- ――
⋅ y - ―――
A = 3 ⋅ ―――
+ 2 ⋅ L ⋅ ⎜y - ―――
⎜⎝
4
2 ⎟⎠
3 ⎜⎝
2 ⎟⎠
⎛⎝2 ⋅ y 2 + 3 ⋅ L 2 ⎞⎠ ⋅ ‾‾
3
A = 3 ⋅ L ⋅ y - ―――――――
6
2 ⋅ ‾‾
3 ⋅ (y - p)
3
4 ⋅ y ⋅ ‾‾
P = 3 L + 2 ⋅ ――――― => P = ―――+ L
3
3
⎛
⎞
3 ⎟ ‾‾
L ⋅ ‾‾
⎜y - ―――
⋅ 3
⎜⎝
2 ⎟⎠
B = 2 L - 2 ⋅ x = 2 L - 2 ⋅ ――――――=>
3
⎛⎝2 ⋅ y 2 + 3 ⋅ L 2 ⎞⎠ ⋅ ‾‾
3
3 ⋅ L ⋅ y - ―――――――
6
A
Rh = ―= ―――――――――
P
‾‾
4⋅y⋅ 3
―――+ L
3
AUX: UNIV. GABRIEL ALZU SOLA
=>
3
2 ⋅ y ⋅ ‾‾
B = 3 L - ―――
3
⎛⎝2 ⋅ y 2 + 3 ⋅ L 2 ⎞⎠ ⋅ ‾‾
3
3 ⋅ L ⋅ y - ―――――――
6
Rh = ―――――――――
‾‾
4⋅y⋅ 3
―――+ L
3
SEMESTRE II/2022
UNIVERSIDAD AUTÓNOMA "TOMÁS FRÍAS"
FACULTAD DE INGENIERÍA
CARRERA DE INGENIERÍA CIVIL
HIDRÁULICA II Y LABORATORIO - CIV 230
FIGURA Nº3
2π
L
L
72 ° = ――
―
―
5
L
L
2
2
= ―――― p = ―――
= ――――
R = ―――
⎛π⎞
⎛π⎞
⎛π⎞
⎛π⎞
π
sin ⎜―
tan ⎜―
36 ° = ―
⎟ 2 ⋅ sin ⎜―
⎟
⎟ 2 ⋅ tan ⎜―
⎟
5
5
5
⎝
⎠
⎝
⎠
⎝
⎠
⎝5⎠
5
Área:
A = 2 ⋅ A4 = 2 ⋅ ⎛⎝A1 - A3⎞⎠
;
1
A1 = ―⋅ (R ⋅ θ) ⋅ R
2
=>
θ ⋅ R2
A1 = ――
2
R2
1
⋅ sin (2 θ)
A3 = ―⋅ R ⋅ sin (θ) ⋅ R ⋅ cos (θ) => A3 = ――
4
2
⎛ θ ⋅ R2
⎞
R2
⋅ sin (2 θ)⎟
A = 2 ⋅ A4 = 2 ⋅ ⎜――- ――
4
⎝ 2
⎠
⎛
⎞2 ⎛
sin (2 θ) ⎞ ⎛
L
sin (2 θ) ⎞
A = R 2 ⋅ ⎜θ - ―――
⎟ = ⎜――――
⎟ ⋅ ⎜θ - ―――
⎟
⎛
⎞
π ⎟ ⎝
2
2
⎝
⎠ ⎜
⎠
2 ⋅ sin ⎜―
⎟
⎜⎝
⎝ 5 ⎠ ⎟⎠
∴
=>
Perímetro: P = 2 R ⋅ θ
2⋅L
⋅θ
P = ――――
⎛π⎞
2 ⋅ sin ⎜―
⎟
⎝5⎠
L
⎛π⎞
2 ⋅ sin ⎜―
⎟
⎝5⎠
L 2 ⋅ (sin (2 ⋅ θ) - 2 θ)
―――――――
Radio
‾‾
5 -5
A
Hidráulico: Rh = ―= ―――――――
P
2
2 ⋅ θ ⋅ L ⋅ ‾‾
――――
‾‾‾‾‾‾‾
- ‾‾
5 +5
=>
2
θ⋅L
2 ⋅ θ ⋅ L ⋅ ‾‾
P = ―――
→ P = ――――
⎛π⎞
‾‾‾‾‾‾‾
sin ⎜―
- ‾‾
5 +5
⎟
⎝5⎠
=>
Espejo de Agua: B = 2 ⋅ R ⋅ sin (θ) = 2 ⋅ ――――
⋅ sin (θ)
L 2 ⋅ (sin (2 ⋅ θ) - 2 θ)
A = ―――――――
‾‾
5 -5
=>
2π
θ ≤ ――
5
2π
θ ≤ ――
5
2 ⋅ sin (θ)
L
2 ⋅ L ⋅ ‾‾
2π
⋅ sin (θ) → B = ――――――θ ≤ ――
B = ―――
⎛π⎞
‾‾‾‾‾‾‾
5
sin ⎜―
- ‾‾
5 +5
⎟
⎝5⎠
‾‾‾‾‾‾‾‾‾‾‾
⎛
⎞
5 ⎠ + 10 ⋅ (sin (2 ⋅ θ) - 2 ⋅ θ)
L ⋅ -⎝2 ⋅ ‾‾
2π
Rh = ―――――――――――― θ ≤ ――
⎛ ‾‾ ⎞
5
4 ⋅ θ ⋅ ⎝ 5 - 5⎠
Profundidad del Flujo:
L
⋅ (1 - cos (θ))
y = R - R ⋅ cos (θ) = ――――
⎛π⎞
2 ⋅ tan ⎜―
⎟
⎝5⎠
FIGURA
Nº4GABRIEL ALZU SOLA
AUX:
UNIV.
=>
-(L ⋅ (cos (θ) - 1))
y = ――――――
‾‾‾‾‾‾‾‾‾‾
⎛
⎞
2 ⋅ -⎝2 ⋅ ‾‾
5⎠+5
2π
θ ≤ ――
5
SEMESTRE II/2022
UNIVERSIDAD AUTÓNOMA "TOMÁS FRÍAS"
FACULTAD DE INGENIERÍA
CARRERA DE INGENIERÍA CIVIL
HIDRÁULICA II Y LABORATORIO - CIV 230
FIGURA Nº4
Área:
1
D
D2
A1 = ―⋅ D ⋅ ―→ A1 = ――
2
3
6
A = A1 + 2 A2 + 2 A3
1 ⎛D ⎞ D
A2 = ―⋅ ⎜―⋅ θ⎟ ⋅ ―
2 ⎝2 ⎠ 2
=>
θ ⋅ D2
A2 = ――
8
1 D
D
A3 = ―⋅ ―⋅ sin (θ) ⋅ ―⋅ cos (θ)
2 2
2
D2
θ ⋅ D2
+ 2 ―― + 2
A = ――
6
8
=>
D2
⋅ sin (2 θ)
A3 = ――
16
⎛ D2
⎞
⋅ sin (2 θ)⎟
⎜――
⎝ 16
⎠
D 2 ⋅ (3 ⋅ sin (2 ⋅ θ) + 6 ⋅ θ + 4)
A = ―――――――――
24
Perímetro:
D
D
D
2 ⋅ ―+ ‾‾
5 ⋅ ―+ 2 ⋅ ―⋅ θ
P = ‾‾
3
3
2
Espejo de Agua:
⎛D
⎞
B = 2 ⋅ ⎜―⋅ cos (θ)⎟
⎝2
⎠
Radio Hidráulico:
Profundidad del Flujo:
=>
=>
⎛ ‾‾
⎞
‾‾
5
2
P = ⎜――
+ ――
+ θ⎟ ⋅ D
⎜⎝ 3
⎟⎠
3
B = D ⋅ cos (θ)
D 2 ⋅ (3 ⋅ sin (2 ⋅ θ) + 6 ⋅ θ + 4)
―――――――――
24
A
Rh = ―= ―――――――――
⎛
⎞
P
‾‾
‾‾
3
2
⎜――
+ ――
+ θ⎟ ⋅ D
3
⎝⎜ 3
⎠⎟
=>
D ⋅ (3 ⋅ sin (2 ⋅ θ) + 6 ⋅ θ + 4)
Rh = ――――――――
8 ⋅ ‾‾
3 + 8 ⋅ ‾‾
2 + 24 ⋅ θ
D D
D ⋅ sin (θ) D
y = ―+ ―⋅ sin (θ) → y = ――― + ―
3
2
2
3
FIGURA Nº5
⎛3⋅π⎞
p = L ⋅ cos ⎜――
⎟
⎝ 10 ⎠
2π
72 ° = ――
5
3⋅π
54 ° = ――
10
Área:
A1 = b ⋅ p
⎛3⋅π⎞
b = L ⋅ sin ⎜――
⎟
⎝ 10 ⎠
⎛3⋅π⎞
(y - p)
q = ―――
y - L ⋅ cos ⎜――
⎟
⎛2 π⎞
⎝ 10 ⎠
sin ⎜――
x = ――――――
⎟
⎛2 π⎞
⎝ 5 ⎠
tan ⎜――
⎟
⎝ 5 ⎠
⎛
⎛ 3 ⋅ π ⎞⎞
⎜y - L ⋅ cos ⎜――
⎟⎟
⎝
⎝ 10 ⎠⎠
q = ――――――
⎛2 π⎞
sin ⎜――
⎟
⎝ 5 ⎠
A = A1 + A2
=>
1
A1 = ―⋅ (2 ⋅ b) ⋅ p
2
⎛3⋅π⎞
⎛3⋅π⎞
A1 = L ⋅ sin ⎜――
⎟ ⋅ L ⋅ cos ⎜――
⎟
⎝ 10 ⎠
⎝ 10 ⎠
⎛3⋅π⎞
L2
⋅ sin ⎜――
A1 = ――
⎟
2
⎝ 5 ⎠
(y - p) GABRIEL ALZU SOLA
AUX:
UNIV.
⋅ (2 ⋅ b + B)
A =
2
―――
2
SEMESTRE
y-p
A2 = ――⋅ (2 ⋅ b + 2 ⋅ b - 2 ⋅ x)
2
II/2022
UNIVERSIDAD AUTÓNOMA "TOMÁS FRÍAS"
FACULTAD DE INGENIERÍA
CARRERA DE INGENIERÍA CIVIL
⎛
2
⎞
L
3⋅π
= ――
⋅ sin
HIDRÁULICA II Y LABORATORIO -ACIV
230
⎜――
⎟
2
⎝ 5 ⎠
1
(y - p)
⋅ (2 ⋅ b + B)
A2 = ―――
2
A2 = (y - p) ⋅ (2 b - x)
=>
=>
B=2 ⋅ b - 2 ⋅ x
y-p
A2 = ――⋅ (2 ⋅ b + 2 ⋅ b - 2 ⋅ x)
2
⎛3⋅π⎞⎞
y - L ⋅ cos ⎜――
⎟⎟
⎛3⋅π⎞
⎝ 10 ⎠ ⎟
L ⋅ sin ⎜――
――――――
⎟
⎛2 π⎞
⎟
⎝ 10 ⎠
tan ⎜――
⎟
⎟
⎝ 5 ⎠
⎠
=>
⎛
⎛
⎛ 3 ⋅ π ⎞⎞ ⎜
A2 = ⎜y - L ⋅ cos ⎜――
⎟⎟ ⋅ ⎜2
⎝
⎝ 10 ⎠⎠ ⎜
⎜
⎝
⎛
⎛3⋅π⎞⎞
y - L ⋅ cos ⎜――
⎜
⎟⎟
⎛3⋅π⎞ ⎛
⎛ 3 ⋅ π ⎞⎞
⎛3⋅π⎞
L
⎝ 10 ⎠ ⎟
A = ――
⋅ sin ⎜――
⎟ + ⎜y - L ⋅ cos ⎜――
⎟⎟ ⋅ ⎜2 L ⋅ sin ⎜――
⎟ - ――――――
⎛2 π⎞
⎟
2
⎝ 5 ⎠ ⎝
⎝ 10 ⎠⎠ ⎜
⎝ 10 ⎠
tan ⎜――
⎟
⎜
⎟
⎝ 5 ⎠
⎝
⎠
2
Perímetro:
⎛
⎛
⎛ 3 ⋅ π ⎞⎞ ⎞
⎜
⎜y - L ⋅ cos ⎜――
⎟⎟ ⎟
⎝
⎝ 10 ⎠⎠ ⎟
=>
P = 2 ⋅ L + 2 ⋅ q = 2 ⋅ ⎜L + ――――――
⎛2 π⎞
⎜
⎟
sin
――
⎜
⎟
⎜
⎟
⎝ 5 ⎠
⎝
⎠
⎛
⎛
⎛ 3 ⋅ π ⎞⎞ ⎞
⎜
⎜y - L ⋅ cos ⎜――
⎟⎟ ⎟
⎝
⎝ 10 ⎠⎠ ⎟
P = 2 ⋅ ⎜L + ――――――
⎛2 π⎞
⎜
⎟
sin ⎜――
⎟
⎜
⎟
⎝ 5 ⎠
⎝
⎠
⎛
⎛
⎛ 3 ⋅ π ⎞⎞ ⎞
⎜
⎜y - L ⋅ cos ⎜――
⎟⎟ ⎟
⎝
⎝ 10 ⎠⎠ ⎟
P = 2 ⋅ ⎜L + ――――――
⎛2 π⎞
⎜
⎟
sin ⎜――
⎟
⎜
⎟
⎝ 5 ⎠
⎝
⎠
Espejo de Agua:
⎛
⎛3⋅π⎞⎞
⎛
⎛3⋅π⎞⎞
y - L ⋅ cos ⎜――
y - L ⋅ cos ⎜――
⎜
⎟⎟
⎜
⎟⎟
⎛3⋅π⎞
⎛3⋅π⎞
10
⎝
⎠
⎝ 10 ⎠ ⎟
⎟ => B = 2 ⋅ ⎜L ⋅ sin ⎜――
- ――――――
B = 2 ⋅ b - 2 ⋅ x = 2 ⋅ ⎜L ⋅ sin ⎜――
⎟ - ――――――
⎟
⎛2 π⎞
⎛2 π⎞
⎜
⎟
⎜
⎟
⎝ 10 ⎠
⎝ 10 ⎠
tan ⎜――
tan ⎜――
⎟
⎟
⎜
⎟
⎜
⎟
⎝ 5 ⎠
⎝ 5 ⎠
⎝
⎠
⎝
⎠
⎛
⎛3⋅π⎞⎞
y - L ⋅ cos ⎜――
⎜
⎟⎟
⎛3⋅π⎞ ⎛
⎛ 3 ⋅ π ⎞⎞
⎛3⋅π⎞
L
⎝ 10 ⎠ ⎟
⎜
+
⋅
⋅
⋅
⋅ sin ⎜――
y
L
cos
2
L
sin
――――――
――
――
――
⎟ ⎜
⎜
⎟⎟
⎜
⎟
⎛2 π⎞
⎟
2
⎝ 5 ⎠ ⎝
⎝ 10 ⎠⎠ ⎜
⎝ 10 ⎠
tan ⎜――
⎟
⎜
⎟
A
⎝ 5 ⎠
⎝
⎠
Rh = ―= ――――――――――――――――――――――
⎛
⎛
⎛ 3 ⋅ π ⎞⎞ ⎞
P
⎜
⎜y - L ⋅ cos ⎜――
⎟⎟ ⎟
⎝
⎝ 10 ⎠⎠ ⎟
⎜
2 ⋅ L + ――――――
⎛2 π⎞
⎜
⎟
sin ⎜――
⎟
⎜
⎟
⎝ 5 ⎠
⎝
⎠
2
Radio Hidráulico:
FIGURA Nº6
De la figura Nº3, respecto a la parte inferior circular tenemos:
⎛3⋅π⎞
L
p = L ⋅ cos ⎜――
―
⎟
⎝ 10 ⎠
L
2
= ――――
R = ―――
⎛π⎞
⎛π⎞
π
sin ⎜―
36 ° = ―
⎛3⋅π⎞
⎟ 2 ⋅ sin ⎜―
⎟
⎝5⎠
⎝5⎠
b = L ⋅ sin ⎜――
5
⎟
⎝ 10 ⎠
⎛
⎛ 3 ⋅ π ⎞⎞
3⋅π
⎜y - L ⋅ cos ⎜――
⎟⎟
54 ° = ――
⎝
⎝ 10 ⎠⎠
q = ――――――
10
⎛2 π⎞
sin ⎜――
⎟
⎝ 5 ⎠
2π
72 ° = ――
5
Área:
A = A2 + 2 ⋅ A4
A4 = A1 - A3
De la figura Nº3:
AUX: UNIV. GABRIEL ALZU SOLA
L 2 ⋅ (sin (2 ⋅ θ) - 2 θ)
2π
; θ = ――
2 ⋅ A4 = ―――――――
= 72 °
5
‾‾
5 -5
⎛ ⎛4 π⎞ 4 π⎞
L 2 ⋅ ⎜sin ⎜――
⎟ - ――
⎟ SEMESTRE II/2022
5 ⎠
⎝ ⎝ 5 ⎠
2 ⋅ A4 = ―――――――
‾‾
5 -5
UNIVERSIDAD AUTÓNOMA "TOMÁS FRÍAS"
FACULTAD DE INGENIERÍA
CARRERA DE INGENIERÍA CIVIL
2
(
(
)
)
L ⋅ (sin (2 ⋅ θ) - 2 θ)
2π
= ――
= 72 °
2 ⋅ A = ―――――――
HIDRÁULICA II Y LABORATORIO
- CIV θ230
5
‾‾
4
5 -5
⎛ ⎛4 π⎞ 4 π⎞
L ⋅ ⎜sin ⎜――
⎟ - ――
⎟
5 ⎠
⎝ ⎝ 5 ⎠
2 ⋅ A4 = ―――――――
‾‾
5 -5
2
De la figura Nº5:
A = A2 + 2 ⋅ A4
Perímetro:
⎛
⎛3⋅π⎞⎞
y - L ⋅ cos ⎜――
⎜
⎟⎟
⎛
⎛ 3 ⋅ π ⎞⎞
⎛3⋅π⎞
⎝ 10 ⎠ ⎟
A2 = ⎜y - L ⋅ cos ⎜――
⎟⎟ ⋅ ⎜2 L ⋅ sin ⎜――
⎟ - ――――――
⎛2 π⎞
⎟
⎝
⎝ 10 ⎠⎠ ⎜
⎝ 10 ⎠
tan ⎜――
⎟
⎜
⎟
⎝ 5 ⎠
⎝
⎠
=>
⎛
⎛3⋅π⎞⎞
⎛4 π⎞ 4 π⎞
2 ⎛
y - L ⋅ cos ⎜――
⎟ ⎟ L ⋅ ⎜sin ⎜――
⎟ - ――
⎟
⎛
⎛ 3 ⋅ π ⎞⎞ ⎜
⎛3⋅π⎞
10
5 ⎠
⎝
⎠
⎝
⎝ 5 ⎠
⎜
⎟
+ ―――――――
A = ⎜y - L ⋅ cos ⎜――
⎟⎟ ⋅ 2 L ⋅ sin ⎜――
⎟ - ――――――
⎛2 π⎞
⎟
⎝
⎝ 10 ⎠⎠ ⎜
⎝ 10 ⎠
‾‾
5 -5
tan ⎜――
⎟
⎜
⎟
⎝ 5 ⎠
⎝
⎠
ó:
A = 2 ⋅ L ⋅ y - 0.32492 ⋅ y 2 - 0.366665 ⋅ L 2
⎛ 2π
⎞
2π
+ 2 ⋅ q = 2 ⋅ ⎜R ⋅ ――
+ q⎟
P = 2 ⋅ R ⋅ ――
5
5
⎝
⎠
=>
ó:
Espejo de Agua:
De la figura Nº5:
ó:
Radio
Hidráulico:
⎛
⎛
⎛ 3 ⋅ π ⎞⎞ ⎞
⎜
⎜y - L ⋅ cos ⎜――
⎟⎟ ⎟
L
2π ⎝
⎝ 10 ⎠⎠ ⎟
⋅ ――
+ ――――――
P = 2 ⋅ ⎜――――
⎛π⎞
⎛2 π⎞
⎜
⎟
5
sin ⎜――
⎟
⎟
⎜ 2 ⋅ sin ⎜―
⎟
⎝5⎠
⎝ 5 ⎠
⎝
⎠
P = 0.901851 ⋅ L + 2.102924 ⋅ y
⎛
⎛3⋅π⎞⎞
y - L ⋅ cos ⎜――
⎜
⎟⎟
⎛3⋅π⎞
⎝ 10 ⎠ ⎟
B = 2 ⋅ ⎜L ⋅ sin ⎜――
⎟ - ――――――
⎛2 π⎞
⎜
⎟
⎝ 10 ⎠
tan ⎜――
⎟
⎜
⎟
⎝ 5 ⎠
⎝
⎠
B = 2 ⋅ L - 0.649839 ⋅ y
⎛
⎛3⋅π⎞⎞
⎛ ⎛4 π⎞ 4 π⎞
y - L ⋅ cos ⎜――
L 2 ⋅ ⎜sin ⎜――
⎜
⎟
⎟
⎟ - ――
⎟
⎛
⎛ 3 ⋅ π ⎞⎞
⎛3⋅π⎞
5 ⎠
⎝ 10 ⎠ ⎟
⎝ ⎝ 5 ⎠
⎜
⋅
⋅
⋅
+
y
L
cos
2
L
sin
―――――――
⎜
⎜――
⎟⎟
⎜――
⎟ ――――――
⎛2 π⎞
⎟
⎝
⎝ 10 ⎠⎠ ⎜
⎝ 10 ⎠
‾‾
5 -5
tan ⎜――
⎟
⎜
⎟
A
⎝ 5 ⎠
⎝
⎠
Rh = ―= ――――――――――――――――――――――――
⎛
⎛
⎛ 3 ⋅ π ⎞⎞ ⎞
∴
P
⎜
⎜y - L ⋅ cos ⎜――
⎟⎟ ⎟
L
2
π
⎝
⎝ 10 ⎠⎠ ⎟
2 ⋅ ⎜――――
⋅ ――
+ ――――――
⎛π⎞
⎛2 π⎞
⎜
⎟
5
sin ⎜――
⎟
⎟
⎜ 2 ⋅ sin ⎜―
⎟
⎝5⎠
⎝ 5 ⎠
⎝
⎠
A 2 ⋅ L ⋅ y - 0.32492 ⋅ y 2 - 0.366665 ⋅ L 2
Rh = ―= ―――――――――――
P
0.901851 ⋅ L + 2.102924 ⋅ y
AUX: UNIV. GABRIEL
ALZU SOLA
SOLUCIONARIO
SEMESTRE II/2022
PRÁCTICA Nº2
FLUJO UNIFORME EN CANALES ABIERTOS
Descargar