Formulario AMP for Written Exam

WATERJET

V_{TH =} √(2P/_ρ0) THEORETICAL VELOCITY FROM BERNOULLI 1^st CONST

V_TH,c = √(2L/(γ-1)ρ₀) (1 + γ-1/L)^m THEORETICAL VELOCITY CONSIDERING COMPRESSIBILITY

Ψ = (V_TH,c/V_TH)_L/(4-m)[(4+P/L)^(1-m)-1] COMPRESSIBILITY COEFFICIENT Ψ¹

V_J = C_v · V_TH,c = C_v · Ψ · √(2P/0.001) VELOCITY OF THE JET

C_v = V_S/V_TH,c VELOCITY COEFFICIENT

S₀ = πd_n²/4 NOZZLE CROSS SECTION

S_J = πd_J²/4 JET CROSS SECTION

C_c = S_J/S₀ CONTRACTION COEFFICIENT ≈,062

C_D = Q_w/Q_TH = Ψ · C_v · C_c OVERALL COEFFICIENT OF DISCHARGE

Q_TH = S₀ · V_TH = πd_n²/4 · √(2P/ρ₀)

Q_w = S_J · V_J = C_Cψ · S₀ √(2P/ρ₀) = C_D · S₀ √(2P/ρ₀) · 60 WATER FLOW RATE

ṁ_w = β · Q_w β = 1×000 g/e

BALANCE WITH ABRASIVE

Q_air + Q_w + Q_abr = Q_TOT

ṁ_air · V_air + ṁ_w V_w + ṁ_abr V_abr = (ṁ_air + ṁ_w + ṁ_abr) · V_avg CONSERVATION OF MOMENTUM

R = ṁ_abr/ṁ_w m/m ABRASIVE LOADING RATIO → V_aus = V_w = V_J (1+R)

R = ṁ_w/ṁ_air ABRASIVE LOAD RATE → V_aus = R · V_s

THRUST FORCE

Nommed = a_way · |ΔV₁| = (ṁ*V_in + m_ice) |ΔV₁| [N] - [Kg · m/s²]

|ΔV₁| = |V_in - V_out|

|ΔV₁| = V_{cos θ} - (-V_{cos θ}) = 2V_cosθ

• V_out
• V_in

JET REACTIVE FORCE

Basically the same as above, without objective

F = m_ice · ΔV₁ = βQwZgγcψ_{5 2P}

= _QβQccψ²_rdn² ² _p

POWER

P_INDR = 1/2 mzv²₅ = βQgQwv²₃ = 1/2CcCcψ₄ dn² √^2P

= π. √²

P/ρ = P_INDR [KW]

TAPER AND TRAIL BACK

• If you have to compensate it:
  • angle of entrance of the jet

PRODUCTION

• Text figure
• T_ot
• Transport text + taper + setup
• Comparator - granular growth
• C_piece = c m/piece

OTHER ISSUE

• RAPIDS must be counted twice if you are doing a shape like that: □ 2 Turns out of the head.
• AVAILABILITY is multiplied to the time of work at week T_max = 1000 h
• T_real = P · T_max
• Control if the pump is able to supply all the Q (at all the heads)
• Usually you find [s/piece] then you express it in [s/ week]

USEFUL THINGS

INTERPOLATION

_y = y_A + (x - x_A) / (x_B - x_A) ⋅ (y_B - y_A)

• If you are free to choose in ranges, always maximize V speed. Then, for the other parameters (like gas flow rate), if it is said that in the range the effect is the same, choose the LOWEST value to minimize its cost.
• α = _K / ^{ρ c_p} [m²/s] Thermal diffusivity
• Q = A ⋅ v volumetric flow rate
• E_cost = P ⋅ C = [^ε/_η] ⋅ cost energy
• 1 m³/s = 1000 dm³/s = 1000 l/s
• sec(α) = 1 / cos(α)
• cosec(α) = 1 / sin(α)
• sec(α) = 1 / cos(α)
• y = log f(x) ⇒ y’ = f'(x) / f(x)