How Wall Friction Effects Hopper Angles
by Joseph Marinelli

In my previous article, I discussed measurement of wall friction angles. The wall friction angle for a given bulk material/wall surface combination is calculated from the results of a wall friction test. By the way, the tangent of the wall friction angle is the coefficient of friction between the two materials. From this angle, the hopper angle required to ensure mass flow is determined. Hopper shapes such as cones and wedges, are determined.

A major consideration is that there is no "magic" angle for mass flow. The following is a common statement: "all I have to do to develop mass flow is to design my hopper with an angle of 70º ".

What is wrong with this statement? Mass flow is dependent on the smoothness and steepness of the hopper wall and the properties of the bulk material involved. If I design my hopper for 70º, I may achieve mass flow; but I also run the great risk of promoting funnel flow. Testing is the only reliable way to determine the correct angle for mass flow.

Dr. Andrew W. Jenike in his Bulletin No. 123, provides design charts that are used to convert wall friction angles to hopper angles for both conical and wedge shaped geometry's. These charts are plots of wall friction angles vs. hopper angles. They are categorized by values of "effective angle of friction", (delta), which are listed in 10º increments from 30º to 70º. Delta is a function of your material’s flowability and is easily obtained from flow properties tests. For each value of , there are combinations of wall friction angle, (phi-prime) and hopper angle, (theta).

These charts may be used in several ways; however, the common approach is as follows:

Figure 1 shows a typical conical hopper chart. Hopper angle and wall friction angle values are plotted on the X and Y axes, respectively. Notice that there is an uncertain region that lies between funnel flow and mass f low. The flow pattern within this region should theoretically be mass flow; however, slight differences in material properties or hopper angle due to fabrication, can result in funnel flow. A switch back and forth between mass flow and funnel flow can cause bin vibrations and other problems. This region represents a margin of safety to minimize the above effects.

Figure 1:  Wall Friction Angle vs. Conical Hopper Angle

If, for example, your wall friction value is 20, the resulting hopper angle required for mass flow is determined by reading over to the edge of the uncertain region and then reading down to (in this case) about a 22º from vertical hopper angle. In actuality, Jenike’s charts indicate the outer boundary line and the user has to back off 4º as a safety factor (the uncertain region is not indicated).

Different design charts are used for wedge hoppers (refer to Figure 2.) than for conical hoppers. Notice that there is no uncertain region in this chart as on the conical hopper design chart, because there is no definite boundary line between mass flow and funnel flow in wedge-shaped hoppers. Thus, wedge shaped hoppers are more forgiving than a conical hoppers and can handle materials with a wide range of flowability. You read the chart the same as a conical hopper chart except that you do not have to allow for a safety factor.

Figure 2.  Wall Friction Angle vs. Wedge Hopper Angle

Using the correct hopper angle for mass flow is critical to your design. If you decide to use a different solid in you bin, (even if it is the same material, but from a different vendor), you would be wise to check wall friction values to ensure the proper hopper angle.

Help others by posting your comments, suggestions and experiences with bulk solids feeding or any other materials handling concerns you may have on our On-Line Help Forum.  For past Ask Joe ! Articles, visit the Ask Joe! Archived Articles.

Guest articles for the Ask Joe! Column are always welcome, for more information please contact Joe Marinelli directly at his email address:  joe@solidshandlingtech.com.