Calculations

Calculations

• Ideal tube-bank j and f

  The heat-transfer and friction factors of an ideal tube bank from the pack's coefficients.

  j = a₁ × (1.33 ÷ (p/d_o))^a × Re^a₂, a = a₃ ÷ (1 + 0.14·Re^a₄)

  Heat exchanger rating process/equip/bell.js

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• Bell-Delaware correction factors

  The five factors that correct the ideal coefficient for baffle cut, leakage and bypass.

  Jc = c₀ + c₁·Fc; Jl = p₁(1 − rs) + (1 − p₁(1 − rs))·e^(−p₂·rlm); Jb = e^(−Cb·Fbp·(1 − ∛(2·Nss⁺)))

  Heat exchanger rating process/equip/bell.js

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• Shell-side coefficient (Bell-Delaware)

  The shell-side film coefficient from the ideal bank value and the correction factors.

  h = j × cp × G × Pr^(−2/3) × Jc·Jl·Jb·Js·Jr

  Heat exchanger rating process/equip/bell.js

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• Shells in series

  The overall effectiveness of several identical shells in series.

  z = ((1 − ε₁·Cr) ÷ (1 − ε₁))ⁿ; ε = (z − 1) ÷ (z − Cr)

  Heat exchanger rating process/equip/bell.js

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• Tube sheet as drawing entities

  The shell circle, tube circles and pass lane placed in a drawing.

  drawing value = layout value (m) × scale

  Heat exchanger rating process/equip/bell.js

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• Pump curve fit

  The quadratic head-flow curve through two or three points a person gives.

  H = c₀ + c₁·Q + c₂·Q²; two points: k = (h₁ − h₂) ÷ (q₂² − q₁²)

  Piping network, pumps and compressors process/equip/network.js

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• Net positive suction head available

  The suction head available at a pump above the vapor pressure.

  NPSHa = (P − Pv) ÷ (ρ·g) + z − h_loss

  Piping network, pumps and compressors process/equip/network.js

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• Polytropic head

  The polytropic head and specific power of gas compression.

  Hp = n ÷ (n − 1) × Z·R·T ÷ M × ((P₂ ÷ P₁)^((n−1)/n) − 1)

  Piping network, pumps and compressors process/equip/network.js

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• Surge margin

  How far a compressor's operating flow is from the surge line at its head.

  margin = (Q − Q_surge(H)) ÷ Q_surge(H)

  Piping network, pumps and compressors process/equip/network.js

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• Greitzer B parameter

  A number that indicates whether a compression system tends to surge or stall.

  B = U ÷ (2·a_s) × √(Vp ÷ (Ac·Lc))

  Piping network, pumps and compressors process/equip/network.js

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• Control valve Kv at an opening

  The flow coefficient of a control valve at a given opening.

  equal percentage: Kv = Kvs × R^(x − 1); linear: Kvs × x; quick opening: Kvs × √x

  Piping network, pumps and compressors process/equip/network.js

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• Head loss of a link

  The head (or pressure-squared) loss of a pipe, pump, valve or control valve at a flow, and its slope.

  liquid: h = (f·L ÷ D + K) × Q·|Q| ÷ (2g·A²); gas: P₁² − P₂² = (Z·R·T ÷ M)(W ÷ A)²·(f·L ÷ D + K + 2·ln(P₁ ÷ P₂))

  Piping network, pumps and compressors process/equip/network.js

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• Network iteration

  Finds the head at every free node and the flow in every link.

  each pass: Q = c₀ + g·(H_a − H_b), g = 1 ÷ (dh/dQ); solve Σ g·(H_i − H_n) = −demand ± c₀

  Piping network, pumps and compressors process/equip/network.js

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• Node pressures and link results

  Pressure at each node and flow, mass flow, velocity and pressure drop of each link.

  liquid: P = (H − z)·ρ·g; gas: P = √(P²); v = Q ÷ A

  Piping network, pumps and compressors process/equip/network.js

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• Compressor head, power and outlet temperature

  Isentropic and polytropic head, both efficiencies, shaft work, power and discharge temperature.

  Hs = (Z·R·T₁ ÷ M) × (k ÷ (k − 1)) × (r^((k−1)/k) − 1); Hp = (Z·R·T₁ ÷ M) ÷ m × (r^m − 1); T₂ = T₁·r^m

  Piping network, pumps and compressors process/equip/compressor.js

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• Operating point against the surge line

  The surge margin of a compressor run, with the head converted to the unit of the map.

  H(m) = Hp ÷ g

  Piping network, pumps and compressors process/equip/compressor.js

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• Pressure wave speed

  The speed of a pressure wave in a liquid inside an elastic pipe.

  a = √((K ÷ ρ) ÷ (1 + (K·D ÷ E·e)·c₁))

  Water hammer and pump trip process/equip/network.js

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• Joukowsky pressure rise

  The pressure rise for an instant change of velocity.

  ΔP = ρ × a × ΔV

  Water hammer and pump trip process/equip/network.js

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• Valve closure transient

  Head and flow at the valve over time, and the highest and lowest head, when a valve at the end of a pipe opens or closes.

  H_P = (C⁺ + C⁻) ÷ 2; Q_P = (C⁺ − C⁻) ÷ 2B; valve: q = (−B·c + √(B²c² + 4c·C⁺)) ÷ 2

  Water hammer and pump trip process/equip/network.js

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• Fitting loss, 2-K form

  The loss coefficient of a fitting from its two constants, the Reynolds number and the pipe diameter in inches.

  K = K₁ ÷ Re + K∞ × (1 + 1 ÷ D)

  Water hammer and pump trip process/equip/transient.js

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• Fitting loss, 3-K form

  The loss coefficient of a fitting from its three constants.

  K = K₁ ÷ Re + Kᵢ × (1 + K_d ÷ D^0.3)

  Water hammer and pump trip process/equip/transient.js

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• Pump trip transient

  Head, flow and pump speed over time after a pump loses power, and when the check valve closes.

  H = α²·h(Q ÷ α), α = ω ÷ ω₀; I·dω/dt = −ρ·g·Q·H ÷ (η·ω)

  Water hammer and pump trip process/equip/transient.js

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• Pipe section properties

  Metal area, second moment of area, torsion constant and section modulus of a pipe.

  A = π(D² − d²) ÷ 4; I = π(D⁴ − d⁴) ÷ 64; J = 2I; Z = I ÷ (D ÷ 2)

  Pipe stress checks process/equip/pipestress.js

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• Tee stress intensification

  The stress intensification factors of a welding, reinforced or unreinforced tee.

  i_o = max(0.9 ÷ h^(2/3), 1); i_i = max(0.75·i_o + 0.25, 1); welding tee h = 4.4·T ÷ r

  Pipe stress checks process/equip/pipestress.js

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• Bend stress intensification and flexibility

  The flexibility characteristic, stress intensification factors and flexibility factor of a bend.

  h = t·R₁ ÷ r²; i_i = 0.9 ÷ h^(2/3); i_o = 0.75 ÷ h^(2/3); k = 1.65 ÷ h

  Pipe stress checks process/equip/pipestress.js

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• Bend tangent points

  Replaces each corner of the run by the two tangent points of a bend of the given radius.

  θ = acos(u₁ · u₂); tangent length a = R₁ × tan(θ ÷ 2)

  Pipe stress checks process/equip/pipestress.js

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• Node stations along the run

  Places a node at every corner, support and tee by its distance along the run.

  s = Σ segment lengths; key = s rounded to 0.001 mm; point = a + f × (b − a)

  Pipe stress checks process/equip/pipestress.js

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• Weight and thermal loads

  The contents and insulation weight per length and the forces that represent free thermal expansion.

  w = ρ_c × 10⁻⁹ × (π ÷ 4)·d² × g + (kg/m ÷ 1000) × g; F = E × A × α × ΔT

  Pipe stress checks process/equip/pipestress.js

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• Stress at each node

  The bending, torsion and axial stress at each node for the sustained, expansion and occasional cases.

  expansion: S_E = √(S_b² + 4·S_t²), S_b = √((i_i·M_i)² + (i_o·M_o)²) ÷ Z, S_t = T ÷ 2Z; M_i = √(M_b² − M_o²)

  Pipe stress checks process/equip/pipestress.js

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• Stress ratios against the allowables

  Sustained, expansion and occasional stress as a fraction of what is allowed.

  S_L = bending + P·D ÷ 4t; S_A = f·(1.25·S_c + 0.25·S_h) + max(0, S_h − S_L); occasional limit 1.33·S_h

  Pipe stress checks process/equip/pipestress.js

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• Free thermal growth

  How much the developed length of the run would grow if it were free.

  growth = ΔT × α × (s_last − s_first)

  Pipe stress checks process/equip/pipestress.js

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• Support lift-off and friction

  Releases rests that would have to pull the pipe down and applies sliding friction at the rests that stay in contact.

  release when R_z(weight) + R_z(thermal) < −10⁻⁶ N; F = −µ·N·(u ÷ |u|), relaxed by 0.6 per pass

  Pipe stress checks process/equip/pipestress.js

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• Nozzle loads

  The force and moment a support passes to the equipment, with a check against a limit.

  F = √(Fx² + Fy² + Fz²); M = √(Mx² + My² + Mz²)

  Pipe stress checks process/equip/pipestress.js

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• Fire coefficient in SI units

  Converts the pool-fire coefficient from Btu/h per ft^1.64 to W per m^1.64.

  C_SI = C_US × 0.29307107 × (1 ÷ 0.3048²)^0.82

  Relief valve sizing, depressuring and flare loads process/equip/relief.js

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• Gas and vapor orifice area

  The orifice area a relief valve needs for a gas or vapor flow.

  A = W ÷ (Kd·Kb·Kc × G); critical: G = P₁·√(k·M ÷ Z·R·T) × (2 ÷ (k + 1))^((k+1)/(2(k−1)))

  Relief valve sizing, depressuring and flare loads process/equip/relief.js

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• Liquid orifice area

  The orifice area for a liquid flow, with the viscosity correction.

  A = Q ÷ (Kd·Kw·Kc·Kv) × √(ρ ÷ 2ΔP); Kv = 1 ÷ (0.9935 + 2.878 ÷ √Re + 342.75 ÷ Re^1.5)

  Relief valve sizing, depressuring and flare loads process/equip/relief.js

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• Critical pressure ratio, omega method

  The pressure ratio at which a flashing two-phase flow chokes.

  η² + (ω² − 2ω)(1 − η)² + 2ω²·ln η + 2ω²(1 − η) = 0

  Relief valve sizing, depressuring and flare loads process/equip/relief.js

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• Two-phase mass flux

  The mass flux of a flashing mixture through a nozzle.

  G = √(P₀·ρ₀) × √(2[ω·ln(1 ÷ η) − (ω − 1)(1 − η)]) ÷ (ω(1 ÷ η − 1) + 1)

  Relief valve sizing, depressuring and flare loads process/equip/relief.js

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• Fire heat input

  The heat a wetted vessel absorbs in a pool fire.

  Q = C × F × A^0.82

  Relief valve sizing, depressuring and flare loads process/equip/relief.js

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• Wetted surface of a vessel

  The vessel surface in contact with liquid up to the fire height.

  vertical: π·D·level + k·D²; horizontal: r·θ·L + 2k·D²·(h ÷ D), θ = 2·acos(1 − h ÷ r)

  Relief valve sizing, depressuring and flare loads process/equip/relief.js

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• Tube rupture flow

  The flow through broken tube ends from the high-pressure side to the low-pressure side.

  Q = Cd × A × √(2(P_h − P_l) ÷ ρ), A = n × π·d² ÷ 4

  Relief valve sizing, depressuring and flare loads process/equip/relief.js

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• Standard orifice letter

  The smallest standard orifice whose area covers the required area.

  in² = m² ÷ 0.0254²

  Relief valve sizing, depressuring and flare loads process/equip/relief.js

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• Flare radiation distance

  The distance from a flare at which the heat flux falls to an allowable level.

  D = √(τ·F·Q ÷ (4π·K))

  Relief valve sizing, depressuring and flare loads process/equip/relief.js

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• Flare header back pressure

  The back pressure at each relief valve as a fraction of its set pressure.

  fraction = (P_back − 101325) ÷ P_set

  Relief valve sizing, depressuring and flare loads process/equip/relief.js

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• Steam orifice area

  The orifice area for steam relief.

  A[in²] = W[lb/h] ÷ (51.5 × P₁[psia] × Kd·Kb·Kc·Kn·Ksh)

  Relief valve sizing, depressuring and flare loads process/equip/relief.js

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• Discharge reaction force

  The thrust on a valve outlet discharging a sonic gas jet to the atmosphere.

  F = W·v + (P_e − P_a)·A_e; v = √(2k·Z·R·T ÷ ((k + 1)·M))

  Relief valve sizing, depressuring and flare loads process/equip/relief.js

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• Outlet line back pressure

  The pressure at the valve outlet for a gas flow through the discharge pipe, and the exit Mach number.

  P₁² − P₂² = (G²·Z·R·T ÷ M) × (f·L ÷ D + K + 2·ln(P₁ ÷ P₂))

  Relief valve sizing, depressuring and flare loads process/equip/relief.js

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• Vessel depressuring curve

  Pressure, temperature and vent flow of a gas-filled vessel over time as it is vented, and the time to reach a target pressure.

  dm/dt = −ṁ; m·cv·dT/dt = Q − ṁ·Rs·T; P = m·Rs·T ÷ V

  Relief valve sizing, depressuring and flare loads process/equip/relief2.js

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• Control valve failure load

  The relief load when a control valve fails open, less the normal flow.

  liquid: Q[m³/h] = Kv × √(ΔP[bar] ÷ SG), ṁ = Q ÷ 3600 × SG × ρ_w; load = max(flow − normal, 0)

  Relief valve sizing, depressuring and flare loads process/equip/relief2.js

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• Header load per case

  The total load on each flare header for each case, and the governing case.

  load = Σ device loads of the scenarios in the case; governing = largest load

  Relief valve sizing, depressuring and flare loads process/equip/relief2.js

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