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
