Metal Casting Gating Design, Bernoulli Mold Aspiration Prevention & Pouring Time
Foundry Tapered Sprue Choke & Aspiration Ratio Formula
Calculate Aspiration-Free Top Sprue Entry Area A1 = A2*SQRT(h2/h1) (mm²), Torricelli Choke Velocity (m/s), Volumetric Pouring Rate (cm³/s), and Mold Fill Time (s).
A straight-sided cylindrical downsprue pulls sub-atmospheric vacuum—sucking air and moisture right through permeable green sand into molten metal!
As liquid metal accelerates downward from Pouring-Basin Depth `h_1` (mm) through Total Metallostatic Head `h_2` (mm) to the sprue base choke, continuity `A_1 * v_1 = A_2 * v_2` causes stream cross-section to contract! If a foundry patternmaker cuts a straight-walled cylindrical downsprue (`A_1 = A_2`), Bernoulli’s equation forces static pressure inside the sprue below `1` atm—aspirating air, steam, and oxide dross through porous sand walls (`pinhole porosity` & `slag inclusions`)! Setting gauge static pressure `P_1 = P_2 = 0` everywhere along the free-falling stream (`v_1 = SQRT(2*g*h_1)` and `v_2 = SQRT(2*g*h_2)`) proves the sprue MUST taper downward with Top Entry Area `A_1 = A_2 * SQRT(h_2 / h_1)`! At the bottom Choke Area `A_2` (mm²) with nozzle friction `C_d` (`~0.78–0.88`), Choke Velocity is `v_choke = C_d * SQRT(2 * g * (h_2 / 1,000))` (m/s), filling Casting + Riser Volume `V_mold` (cm³) in `t_pour = V_mold / Q_cm3_s` seconds!
Verify on a Bottom-Choked Aluminum Sand Mold—Pouring_Cup_Metal_Head `h_1` = 65.0 mm (B2), Total_Sprue_Base_Head `h_2` = 260.0 mm (`h_2 / h_1 = 4.0`, B3), Sprue_Base_Choke_Area `A_2` = 320.0 mm² (B4 -> Required Tapered Top Area `A_1 = 320 * SQRT(4) = 640.00` mm² in E2), Gating_Discharge_Coeff `C_d` = 0.82 (B5 -> Choke Velocity = `1.85` m/s in E3 & Flow = `592.6` cm³/s in E4), and Total_Poured_Volume `V_mold` = 4,800.0 cm³ (B6): Mold Fill Time equals `8.10` seconds (E5)!
| Foundry Gating Sprue KPI (h1=65 mm, h2=260 mm, Choke A2=320 mm², Cd=0.82, V=4,800 cm³) | Formula | Verified Output |
|---|---|---|
| Aspiration-Free Top Area A1 (mm²) | Choke_Area_A2 * SQRT(Total_h2 / Cup_h1) | 640.00 mm² (846.64 mm² @ tall 455 mm sprue) |
| Bernoulli Choke Velocity (m/s) | Cd * SQRT(2 * 9.80665 * (h2_mm / 1000)) | 1.85 m/s (2.45 m/s @ tall 455 mm sprue) |
| Volumetric Pouring Rate (cm³/s) | (A2_mm2 / 100) * (Choke_Vel_m_s * 100) | 592.6 cm³/s (783.9 cm³/s @ 455 mm) |
| Total Mold Pouring Time (sec) | Casting_Plus_Riser_cm3 / Flow_Rate_cm3_s | 8.10 s (6.12 s @ tall 455 mm sprue) |
Zero-Aspiration Parabolic Sprue Taper & Torricelli Choke Fill-Time Formula
Validate `Cup_Head h_1 > 10` mm, `Total_Head h_2 > h_1`, `Choke_Area A_2 > 0` mm², `Discharge_Coeff C_d` in `[0.40, 1.0]`, and `Mold_Volume > 0` cm³!
=LET(hc_m, B2, ht_m, B3, ac_m, B4, cd_g, B5, vm_c, B6, IF(OR(hc_m <= 10, ht_m <= hc_m, ac_m <= 0, cd_g < 0.4, cd_g > 1, vm_c <= 0), "Invalid Sprue Input", LET(vc_s, cd_g * SQRT(2 * 9.80665 * (ht_m / 1000)), qf_c, ac_m * vc_s, ROUND(vm_c / qf_c, 2))))Tall Cope Flask 455 mm Metallostatic Head Check (Set Total Head h2 B3 = 455.0 mm)
Pour a deeper cope flask raising `h_2` B3 from `260.0` to `455.0` mm (`h_2 / h_1 = 7.0`): Required Top Entry Area `A_1` E2 widens to `846.64` mm² (`2.646x` choke area to prevent vacuum aspiration!), Choke Velocity E3 accelerates to `2.45` m/s, Flow Rate E4 reaches `783.9` cm³/s, and Pour Time E5 shortens to `6.12` s!
=IF(ISTEXT(E5), E5, ROUND(B4 * SQRT(B3 / B2), 2))Try the example
Use the original values or change them to test your understanding.