Abstract
A new formulation has been developed to describe the fluid dynamics of a liquid draining through an orifice under the influence of gravity. The model relates experimental quantities of head and flow rate, with surface tension, viscosity, and density, facilitating the calculation of all three properties. Experiments performed with molten aluminum at temperatures from 937 to 1173 K indicate that surface tension (N/m) and density (kg/m3) are [0.871 − 0.155 × 10−3 (T − T liq)] and [2390 − 0.15 (T − T liq)], which is within 6.5 and 2.5 pct, respectively, of values reported in the literature. The viscosity has been determined to be 5.2 × 10−4 Nsm−2, which is significantly less than data reported from other sources. The method is unique because the measurements are performed under highly dynamic conditions.
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Abbreviations
- A :
-
constant in Arrhenius’ formula (Pa s)
- a :
-
polynomial constant describing slope of the discharge coefficient curve (no units)
- B :
-
constant in Arrenius’s formula (J/mole)
- b :
-
polynomial constant describing the y-intercept of the discharge coefficient curve (no units)
- C d :
-
discharge coefficient (no units)
- C m :
-
cumulative mass (kg)
- ΔE :
-
vector describing the error in experimental and calculated head values for regression analysis (m)
- g :
-
gravitational constant (m/s2)
- h :
-
liquid head above a point of reference (m)
- M :
-
molecular weight (kg/mole)
- Q :
-
volumetric flow rate (m3/s)
- R:
-
gas constant (8.3144 J/mol)
- Re:
-
Reynolds number (no units)
- r :
-
radius (m)
- T :
-
temperature (K)
- t :
-
time (s)
- u :
-
velocity (m/s)
- Δx :
-
vector describing change in surface tension, viscosity, or density for regression analysis
- V exp :
-
mass flux of melt (kg/m2 s)
- Z :
-
matrix of partial derivatives for regression analysis
- Y :
-
vector describing difference between experimental head and calculated head for regression analysis (m)
- z :
-
distance on z-axis (m)
- δ :
-
error in a measurement; also represents standard deviation
- ε :
-
tolerance for regression analysis (no units)
- η :
-
viscosity (Nsm−2)
- ρ :
-
density (kg/m3)
- σ :
-
surface tension of liquid (N/m)
- Al:
-
aluminum
- exp:
-
experimental
- i :
-
sample number ‘i’
- j :
-
iteration number for mutiple nonlinear regression analysis
- liq:
-
liquidus
- n :
-
sample number
- o :
-
orifice
- v :
-
vessel
- η :
-
viscosity
- ρ :
-
density
- σ :
-
surface tension
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Roach, S.J., Henein, H. A new method to dynamically measure the surface tension, viscosity, and density of melts. Metall Mater Trans B 36, 667–676 (2005). https://doi.org/10.1007/s11663-005-0057-5
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DOI: https://doi.org/10.1007/s11663-005-0057-5