The Beverloo Hourglass: Understanding Sand Flow Dynamics |…

What is the Beverloo Hourglass?

The Beverloo Hourglass simulates a 2D hourglass where sand flows from one chamber to another. This simulation demonstrates the Beverloo discharge law, which describes how the flow rate of granular materials through an opening depends on the width of the neck and the size of the grains.

By adjusting parameters like neck width, grain size, and the number of grains, users can observe how these factors influence the sand's movement and settle into a pile at a specific angle-of-repose.

Why Does It Matter?

Understanding the Beverloo discharge law is crucial in various fields such as mining, construction, and environmental science. It helps engineers design better hourglasses or predict how granular materials will behave under different conditions.

The simulation also aids in studying the mechanics of granular flows, which are relevant to natural phenomena like avalanches and landslides.

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How Does the Beverloo Discharge Law Work?

According to the Beverloo discharge law, the flow rate (Q) through a narrow opening is proportional to the square root of the neck width (w) and inversely proportional to the grain size (d). This relationship can be expressed as Q ∝ w^(1/2)/d. The law provides a simple yet effective way to predict the behavior of granular materials in confined spaces.

The simulation uses this principle to compute the flow rate live, showing how changes in neck width and grain size affect the sand's movement.

Real-World Applications

The Beverloo discharge law is applied in industrial processes where granular materials need to be transported or sorted. For instance, it helps in designing efficient conveyors for bulk material handling and in understanding the dynamics of sand dunes in desert environments.

In everyday life, this principle can explain why some hourglasses run faster than others based on their design.

Frequently asked questions

What is the angle-of-repose?

The angle-of-repose is the maximum angle at which a granular material can be piled without sliding. In the simulation, it determines how the sand settles into a pile.

How does changing the neck width affect the flow rate?

Increasing the neck width generally increases the flow rate because the grains have more space to move through, but only up to a point. Beyond that, other factors like grain size become more significant.

Why is the fine/coarse sand toggle important?

It changes the grain size of the sand, which directly affects the flow rate and how the grains move through the neck. Fine grains have a smaller diameter and can pass through narrower openings more easily than coarse grains.

What does the flip button do in the simulation?

The flip button simulates the process of flipping the hourglass, causing the sand to flow from one chamber to another. This action demonstrates the Beverloo discharge law in real-time.

Try it live

Everything above runs in your browser — open Beverloo Hourglass Sand Flow (2D) and change the parameters while it is running. Nothing is installed, nothing is uploaded, the whole model lives in one tab.

▶ Open Beverloo Hourglass Sand Flow (2D) simulation