Esercizi fluidodinamica, prof. Andrea Crivellini

DINAMICA

d = 0,13 [m] D = 0.3 [m] U₀ = 40 [m/s] V = 0,42 [m³] θ = 30° P_S = 2,5 ϱ [P₀] P₀ = P_atm = 1,05 * [P₀]

CON MASSA

ϱU₁A₁ + ϱU₂A₂ = ϱUA₀ => 2ϱUA₁ = ϱUA₀

U₁ = U₂ = U U₀ = (U A₀) / 2A = 13,9 [m/s]

BERNOULLI

P_S + ϱgz + ϱ(U₀²)/2 = P + ϱz + ϱ(U²)/2

P = (P_S + (U₀²) / 2 ϱ) = 253395 [P₀] P_b = P - P_atm = 53335 [ϱ]

P₀ = P_atm

QUANTITÀ DI MOTO

ϱU₁A₁Û + ϱU₂A₂U₂ + ϱU A₀Û = ϱA_n U₁ - ϱ₂A₂n₂ + ϱA_nÛ - F_x

F_x = +2ϱ₁A₁cosθ + 2ϱ₁A₁ cosθ - ϱU²A₀ = 2 (-ϱ_n1A₁cosθ) = F_x

F_x = +2 ϱ₁A₁ cosθ + 2ϱ₁A₁ cosθ ϱU²A₀ = 3800 [N]

Y: Fy = ρgV = u120 [N]

Statica

Calcolare per quali p₁ lo sforzo risulta in equilibrio

• H = 6.3 [m]
• h = 4.1 [m]
• l = 3.2 [m]
• θ = 22°
• ρ₀ = 1000 [kg/m³]

1. S_o,0 = (ϱ₀g ^h/₂) h/l_m1 b = 220,105.7 [N]

   M₁ = 85128.7 [Nm]

2. C_o,0 = 2/3 h / l_m1 = 3.64 [m] + l_calθ

3. S_i,0 = (ϱi g ^h/₂) h/l_m0 b = ?

   M₃

4. C_i,0 = 2/3 1 / l_m0 = 5.6 [m] + l_calθ

5. S_0,v = ϱ₀ g h . l . b = 223707 [N]

   C_0,v = l/2 = 1.6 [m]

6. S_i,v = ϱi g h . l = ?

7. C_i,v = l/2 = 1.6 [m]

l_m

M₁/h₂ = M₃ + M₄

1007 + 123 = ((ϱ₀g ^h/₂) l_m0 b) - 5.6 + (ϱ₀g h l _b) 1.6

=> ϱ₀g ^h/₂ l_m0 5.64 ϱi g h l _b 1.6 = 1007 + 113

>= p₁ = 312.11 [N/m²] 3.623 [N/m]

Statica

• Manometro
• P_atm = 1 bar
• P_int = P_atm + P_man = 9 bar

h₁ = 6 [m]

h₂ = 1 [m]

h₃ = 2 [m]

b = 1.5 m

P_int = P_n - ρg (h₂ + h_a) = 350850 [Pa]

h_a = ^P_atm⁄_γ = 86.74 [m]

h_tot = h_a + h₂ + h₃ = 89.74 [m]

S₁ = ρg (89.74 + 1.5) · 3 · b = 23308313.2 [N]

Y_G,1 = 82.74 + 1.5 = 84.24 [m]

I₁ = ^b³⁄₁₂ = 2.25 [m²]

A₁ = 3 · b = 3 [m²]

Y_CP,1 = 84.24 + ^2.25⁄_{84.24 · 3} = 84.2489 [m]

b₁ = Y_CP,1 - 82.7 = 1.5089 [m]

Π₁ = 3607826.2 [N · m]

STATICA

ρ₁ = 1200 [ _kg/_m³ ]

ρ₂ = 3000 [ _kg/_m³ ]

h_t = 1.2 m

h_r = 1.3 m

b = 2 m

l = 2 m b = 2 m

Calcolare il momento rispetto a A

L = ᵃᵐ⁴⁵ = 2√2 = 2.3 [m]

PCI: ρ₁ h* = ρ₂ h^* -> h^* = ρ₂ 1_ρ1.3 = 0.6 [m]

y_c, = tᵏᵐ⁴⁵ / 1 = 2.26 [cm]

• I = b_L = 2√2 [m²]
• A = b_L = 2√2 [m²]

y_cp = 2.26 + ^1.39/_2.26 2√2 = 2.55 [m]

d = y_cp - ^tᵏ/_ᵐ⁴⁵ = 1.7 [m]

S = q ( h^* + ^{ᶫ/2 ) A = 133.256 [N]}

M = S.b = 226.414 [N.m]

Statica

h₁ = 4 [m]

h₂ = 2 [m]

l = 4 [m]

ρ = 1,000 [kg/m³]

Ma?

S₁ = ρg (h₁ + ^h₂⁄₂) h₁^m₆₀ b = 1132761 [N]

γ₆ = ^l⁄_m60 + ^h₂⁄_2m60 = 10√3/3 = 5.77 [m]

I = (^l⁄_m60) / 12 = (6√3 / 27) = 1.026 [m²]

A = ^h₂⁄_m60 5 = 4√3/3 = 2.32 [m²]

b₁ = ^h₂⁄_2m60 + I / Aγ₆ = 1.23 [m]

S₂ = ρg (h₁ + h₂) l • b = 235, 649 [N]

b₂ = ^l⁄₂ • 1.15 = 0.35 [m]

S₃ = ρg (hu_2b) (hi_nt_ed) • b = 176,580 [N]

b = ^2/3 • 6 - u = 0 [m]

M_A = S₂ • b₂ + S₁ • b = 339, 653.5 [Nm]