Hopper design workspace.
Turn measured flow-function, wall-friction and density regressions into an iterative mass-flow boundary, cohesive-arching outlet, Janssen stress estimate and funnel-flow rathole check. Every fitted coefficient and design step remains visible.
01Measured-property regressions
Coefficients below reproduce the supplied workbook example. Replace them with regressions from representative tests. Stress is in kPa, angles in degrees and density in kg/m³.
Fit paired test data to a selected model
Paste one stress,value pair per line. Commas, semicolons, tabs and spaces are accepted. Review the fitted curve and extrapolation range outside this workspace before design use.
02Mass-flow hopper design
The solver iterates wall friction, the mass-flow boundary and Jenike flow factor at the governing stress. Hopper half-angle is measured from vertical.
03Janssen stress & rathole diameter
A numerical Janssen integration estimates vertical consolidation stress. The critical stable rathole diameter is then evaluated from cohesive strength and the static angle of internal friction.
DF = 4.3 tan(φt) · P fc /(ρbg)
04Hopper geometry & capacity
Uses the calculated mass-flow hopper angle. For plane-flow geometry, the result is a wedge-prism volume using the entered plan length.
Plane-flow wedge: V = Lh(D + B)/2