Metallostatic Pressure
Calculate the metallostatic pressure exerted by molten metal at the bottom of a mold, P = ρ × g × h, from the molten metal density ρ (kg/m³), gravity g and the metal column height h (m). The result, in pascals, is the pressure the molten metal exerts on the mold walls and bottom due to its own weight — analogous to hydrostatic pressure, but with the high density of metals. It is essential to size the mold strength (which can 'burst' or deform under pressure), predict core flotation and metal penetration into gaps. Dense metals (iron, ~7000 kg/m³) generate high pressures. Enter the metal density and the column height.
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Metallostatic pressure
When a mold is full of liquid metal, that metal — dense and heavy as it is — exerts pressure on the walls and the floor of the mold, exactly as water in a dam exerts hydrostatic pressure. This is metallostatic pressure: P = ρ × g × h, where ρ is the density of the liquid metal (kg/m³), g is gravity and h is the height of the metal column above the point under consideration (measured from the metal level in the pouring basin down to that point). What sets it apart from water is density: liquid metals are very dense (cast iron around 7000 kg/m³, seven times water; copper around 8000; lead around 10,700), so they build up considerable pressures even with modest columns. That pressure carries several practical consequences a foundry engineer must master. Mold strength: the sand mold (or the flask that holds it) has to withstand the pressure without deforming, bursting or letting metal escape through the joints as flash — which is why molding boxes get clamped and sometimes weighted down with ballast on top. Core flotation: cores (the sand pieces that form holes and internal cavities) are less dense than the metal and tend to float and shift under metallostatic pressure (Archimedes buoyancy, with molten metal), so they demand firm anchoring. Metal penetration: the pressure drives liquid metal into the pores and crevices of the sand, causing rough-surface defects. Feeding: the pressure of the metal column in the riser is precisely what pushes metal into the casting during shrinkage. Working out the peak metallostatic pressure (at the base of the mold, with the column full) is essential to size the robustness of the mold and the ballast. Enter the metal density and the column height.
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Calculate the solidification time of a casting by Chvorinov's rule, t = B × (V ÷ A)², from the mold constant B (min/cm², depending on the mold material and metal) and the ratio of the part's volume V to its surface area A. The result, in minutes, is the time for the metal to fully solidify. The rule shows that parts with a higher volume/area ratio (more 'massive') solidify more slowly — a fundamental casting design principle: risers (metal reservoirs) must have a larger modulus than the part to solidify last and feed the shrinkage. Enter the mold constant, the volume and the part area.
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Calculate the fill time of a casting mold, t = V ÷ Q, dividing the cavity volume V by the metal flow rate Q of the gating system. The result, in seconds, is the time to completely fill the mold with molten metal. It is a critical parameter: filling too slowly lets the metal cool and solidify before filling everything (cold shut, misrun defects), while too fast causes turbulence, gas entrapment, mold erosion and inclusions. The optimal time depends on the part's weight and thickness and the metal. Sizing the gating system for the right time is central to casting design. Enter the cavity volume and the flow rate.
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Janssen Characteristic Depth
Calculate a silo's Janssen characteristic depth, z₀ = D ÷ (4·μ·K), from the diameter D, product-wall friction coefficient μ and lateral pressure ratio K. The characteristic depth governs how fast silo pressures approach their asymptotic (limit) value: in the Janssen equation, it is the depth at which pressure reaches about 63% (1 − 1/e) of the maximum. Depths of a few times z₀ practically reach the limit pressure. Conceptually, z₀ shows how 'deep' the silo must be for wall friction to dominate: silos with small z₀ (small diameter, high friction) quickly reach the constant-pressure regime and behave as slender (tall) silos; silos with large z₀ (large diameter) saturate slowly and behave more like squat silos, where much of the weight still reaches the bottom. The characteristic depth is thus a natural measure of the vertical 'scale' of the silo's pressure behavior, useful to classify it and understand its load profile. Enter the diameter, friction coefficient and lateral pressure ratio.
Gate Area
Calculate the gating channel section area, A = Q ÷ v, dividing the desired metal flow rate Q by the metal velocity v. The result, in the consistent area unit (cm²), is the cross-section the sprue (or gate) must have to deliver the needed flow at the calculated velocity. It is the application of the continuity equation to the casting gating system. Correctly sizing the areas of the system's elements (basin, sprue, runner, gates) controls the flow rate, velocity and flow regime of the metal, avoiding turbulence and ensuring proper filling. The ratios between the areas define the system type (pressurized or unpressurized). Enter the flow rate and the velocity.
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The results provided by this tool are for general informational and educational purposes only and do not constitute professional, financial, medical, legal, tax or accounting advice. Always confirm important decisions with a qualified professional and official sources.