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Truncated Hopper Slope Angle Equation:
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The Truncated Hopper Slope Angle is a critical parameter in hopper design that determines the inclination required for proper material flow. It represents the angle between the hopper wall and the vertical axis, calculated based on the geometry of the truncated conical section.
The calculator uses the trigonometric equation:
Where:
Explanation: The equation calculates the angle of inclination by finding the arctangent of the ratio between the difference in radii and the height of the hopper section.
Details: Accurate slope angle calculation is crucial for ensuring proper material flow, preventing arching and ratholing, and optimizing hopper design for various bulk materials in industrial applications.
Tips: Enter all dimensions in meters. Ensure R > r > 0 and h > 0. The calculator will compute the slope angle in degrees.
Q1: Why is the slope angle important in hopper design?
A: The slope angle determines the steepness required for material to flow freely without sticking or bridging, ensuring efficient discharge from the hopper.
Q2: What are typical angle values for different materials?
A: Angle requirements vary by material properties. Free-flowing materials may require angles of 45-55°, while cohesive materials may need steeper angles of 60-70° or more.
Q3: How does wall friction affect the required angle?
A: Higher wall friction materials require steeper angles to overcome friction and ensure reliable flow. Wall friction tests are often conducted to determine optimal angles.
Q4: Can this calculator be used for non-circular hoppers?
A: This calculator is specifically for circular conical hoppers. For rectangular or square hoppers, different calculations are needed based on the geometry.
Q5: What units should be used for input values?
A: All input values should be in meters (m) for consistent results. The calculator will output the angle in degrees.