Velocity of Metal flow in a Sprue - Metal Casting

VELOCITY OF METAL FLOW IN A SPRUE

Green sand casting is one of the simplest and most popular casting processes. The following figure shows the schematic diagram of a simple green sand mold together with all the components of the gating system. 

The gating system of a sand mold consists of pouring basin, sprue, sprue basin, runner, gates, and runner extension. The design of the gating system mainly involves considerations of fluid flow. To avoid formation of casting defects, it is necessary to control the rate of mold filling. Too fast a metal flow causes air entrapment, porosity and dross formation, and erosion of sand, whereas too slow a flow causes the metal to solidify prematurely, yielding defects such as misrun (an incomplete casting) and cold laps (inhomogeneous or layered casting surface). A well-designed gating system evenly distributes the incoming metal to all parts of the mold without causing turbulence or sand erosion.

A pouring basin is either rectangular or square in cross-section, with a fiat base and a fillet at the base near the sprue entrance. Spherical pouring basins with a curved base cause vortex flow and casting defects. A sprue connects the pouring basin to the runner. A sprue is usually tapered to allow for downward laminar flow, and the sprue basin provides space for the metal to dissipate some energy before changing its direction as it flows into the runners.

EXAMPLE

The figure shows a tapered sprue with the metal head H₁ in the pouring basin, and the total metal head, H₂. The cross-sectional areas at the top and the bottom of the sprue are A₁ and A₂. Determine the metal flow velocity at the top and bottom of the sprue. Also derive a relation between heads H₁, H₂ and cross-sectional areas A₁, A₂ of the sprue.

SOLUTION

From the basic fluid mechanics, using Bernoulli’s Principle, we have

The velocity of fluid (v) at a cross-section with head ‘h’ is given by

Metal head at the top of sprue is H₁ and metal head at the bottom of sprue is H₂.

Similarly, considering the metal flow in the gating system,

The metal flow velocity at the top (v_top) of the sprue is given by

The metal flow velocity at the bottom (v_bottom) of the sprue is given by

We know that the fluid mass crossing the areas A₁ and A₂ per unit time is constant i.e. the metal mass flow rate is constant.

So, the mass flow rate (ṁ) at the top of sprue is equal to that at the bottom of the sprue.

Mass flow rate (ṁ) = velocity × density × Area of cross-section

This yields the fundamental relationship A₁√H₁ = A₂√H₂   .