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Dairy & Food Process Engineering, FDA PMO HTST Pasteurization & Sanitary Fluid Flow

HTST Pasteurization Holding-Tube Fastest-Particle Formula

Calculate Sanitary Holding-Tube Mean Bulk Velocity (m/s), Reynolds Number Re, Laminar (2.0x) vs Turbulent (1.22x) Fastest-Particle Residence Time (s), and FDA PMO 15-Second Legal Compliance.

Switch an HTST pasteurizer from turbulent fluid milk to viscous ice-cream mix at the same pump rate and centerline velocity jumps to 2x—cutting legal hold time below 15 seconds!

Under the FDA Grade "A" Pasteurized Milk Ordinance (PMO), continuous High-Temperature Short-Time (HTST, >= 72 °C for >= 15.0 seconds) holding tubes are NOT regulated on Mean Plug-Flow Residence Time `t_avg = L / v_avg`—every single droplet, including the FASTEST centerline streamline `v_max`, must remain inside the upward-sloping sanitary tube for at least 15.0 seconds! In fully turbulent pipe flow (`Re = rho * v_avg * D / mu >= 4,000`, typical of fluid whole/skim milk at 72 °C), radial eddy mixing flattens the velocity profile to `v_max ≈ 1.22 * v_avg`; if high viscosity (`mu`, e.g. heavy cream, eggnog, or ice-cream mix!) drops Reynolds number into laminar Hagen-Poiseuille flow (`Re < 2,100`), the centerline paraboloid accelerates to `v_max = 2.00 * v_avg`—slashing Fastest-Particle Hold Time `t_min = L / v_max` by nearly `39%` at identical volumetric pump L/hr!

Verify on a 5,400 L/h Sanitary Dairy HTST Holding Tube—Product_Flow `Q` = 5,400.0 L/h (B2), Sanitary_Tube_ID `D` = 47.5 mm (`2"` OD x `1.65` mm wall, B3), Holding_Tube_Length `L` = 18.50 m (B4), Milk_Density `rho` = 1,028.0 kg/m³ (B5), and Milk_Viscosity_at_72C `mu` = 1.45 mPa·s (B6): Mean Bulk Velocity equals `0.846` m/s (E2), Reynolds Number hits turbulent `28,506` (E3), Fastest-Particle Residence Time (`v_max = 1.22 * v_avg`) equals `17.91` seconds (E4), and Regulatory Gate confirms `"PMO >= 15s LEGAL PASS"` (E5)!

FDA PMO HTST Holding-Tube KPI (5,400 L/h, ID=47.5 mm, L=18.5 m, mu=1.45 mPa·s)FormulaVerified Output
Mean Bulk Velocity v_avg (m/s)(Q_L_hr / 3600000) / ((PI()/4)*(ID_m^2))0.846 m/s
Holding-Tube Reynolds Number Re(rho * v_avg * ID_m) / (mu_mPa_s / 1000)28,506 (1,181 laminar @ 35 mPa·s mix!)
Fastest-Particle Hold Time (sec)Length_m / (IF(Re<2100, 2.0, 1.22)*v_avg)17.91 s (10.93 s ILLEGAL @ 35 mPa·s!)
FDA PMO >= 15.0 s Legal AuditFastest_Hold_sec >= 15.0PMO >= 15s LEGAL PASS

Hagen-Poiseuille Laminar vs Turbulent HTST Fastest-Particle Hold Time Formula

Validate `Product_Flow > 0` L/h, `Tube_ID > 5` mm, `Tube_Length > 0` m, `Density > 500` kg/m³, and `Viscosity > 0` mPa·s (cP). Put the explicit input guard on `E2` and propagate `ISTEXT(E2)` across `E3..E4` so text audit labels in `E5` stay decoupled from numeric upstream cells!

=LET(qf_l, B2, id_m, B3, ln_m, B4, rh_k, B5, mu_c, B6, IF(OR(qf_l <= 0, id_m <= 5, ln_m <= 0, rh_k <= 500, mu_c <= 0), "Invalid HTST Input", LET(dm_t, id_m / 1000, ar_t, (PI() / 4) * (dm_t ^ 2), va_s, (qf_l / 3600000) / ar_t, re_n, (rh_k * va_s * dm_t) / (mu_c / 1000), vm_x, IF(re_n < 2100, 2 * va_s, 1.22 * va_s), tm_s, ln_m / vm_x, IF(tm_s >= 15, "PMO >= 15s LEGAL PASS", "ILLEGAL UNDER-HOLD (<15s)"))))

Viscous Ice-Cream / Eggnog Mix Laminar Transition Trap Check (Set Viscosity mu = 35.0 mPa·s)

Pump viscous `35.0` mPa·s mix (`B6 = 35`) at the exact same `5,400` L/h positive-displacement timing-pump speed: Mean Velocity E2 stays `0.846` m/s, yet Reynolds Number E3 plunges from `28,506` into laminar `1,181`, doubling centerline peak velocity (`2.0 * v_avg`) so Fastest-Particle Hold Time E4 collapses from `17.91` s down to `10.93` s (`"ILLEGAL UNDER-HOLD (<15s)"` in E5, requiring timing-pump slowdown or longer holding loop)!

=IF(ISTEXT(E2), E2, LET(dm_t, B3 / 1000, ar_t, (PI() / 4) * (dm_t ^ 2), va_s, (B2 / 3600000) / ar_t, re_n, (B5 * va_s * dm_t) / (B6 / 1000), vm_x, IF(re_n < 2100, 2 * va_s, 1.22 * va_s), ROUND(B4 / vm_x, 2)))

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