1. What is a Truncated Hopper Slope Angle Calculator?

Definition: This calculator determines the slope angle (θ) of a truncated conical hopper based on its dimensions.

Purpose: It helps engineers and designers calculate the optimal slope angle for material flow in hoppers and silos.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( \theta \) — Hopper slope angle (degrees)
• \( H \) — Total hopper height (meters)
• \( h \) — Outlet height (meters)
• \( r \) — Hopper radius (meters)

Explanation: The formula calculates the angle of the hopper walls relative to vertical by comparing the height difference to the radius.

3. Importance of Hopper Slope Angle

Details: Proper slope angle ensures material flow without arching or rat-holing, critical for bulk material handling systems.

4. Using the Calculator

Tips: Enter the total hopper height, outlet height, and radius in meters. All values must be positive, and hopper height must be greater than outlet height.

5. Frequently Asked Questions (FAQ)

Q1: What's a typical hopper angle for free-flowing materials?
A: Most materials require 55-65° from horizontal (25-35° from vertical) for reliable flow.

Q2: How does outlet height affect the angle?
A: Higher outlets create steeper angles, while lower outlets create shallower angles for the same total height.

Q3: What if my hopper is rectangular instead of circular?
A: Use the equivalent radius (half the diagonal dimension) for rectangular hoppers.

Q4: Does this account for material properties?
A: No, this calculates geometric angle only. Actual required angle depends on material flow properties.

Q5: How precise should these measurements be?
A: For most applications, measurements to the nearest centimeter (0.01m) are sufficient.