Bivariate Normal Distribution Funnel for Blockage Prevention
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Solution Overview
Problem
Conventional funnels often experience blockages and inefficiencies due to their design focusing primarily on volume rather than transport efficiency, leading to issues during the flow of liquids, powders, and granules.
Innovation Solution
A bivariate normal distribution funnel is designed with a smooth funnel body formed by rotating a normal distribution curve around the z-axis, combined with a conical outlet tube, ensuring continuous smoothness and reducing resistance for fluid flow.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Volume of stationary object
If the funnel body is designed with a conventional conical shape focusing on volume, then the volume capacity is improved, but the transport efficiency deteriorates causing blockage and overflowing
Solution Approach 1:
The patent applies parameter changes by transitioning from a conventional conical funnel shape to a bivariate normal distribution shape. This mathematical transformation optimizes the geometric parameters of the funnel body, creating a profile that naturally guides material flow while maintaining adequate volume capacity. The bivariate normal distribution provides optimal curvature transitions that prevent blockage while preserving storage capacity.
Solution Approach 2:
The patent utilizes curvature principles by employing a bivariate normal distribution shape, which features smooth, continuous curved surfaces without sharp edges or angles. This curved geometry promotes uniform material flow through the funnel, preventing stagnation and blockage while maintaining efficient transport capability. The smooth curvature transitions are key to improving productivity without sacrificing volume.
2Ease of manufacture
If the funnel body has conventional design with sharp edges and angles, then the manufacturing simplicity is improved, but the fluid flow resistance increases causing blockage
Solution Approach 1:
The patent eliminates sharp edges and angles by adopting a bivariate normal distribution shape, which inherently provides smooth, continuous curved surfaces throughout the funnel body. This curved geometry ensures uniform material flow and prevents blockage by eliminating points where material could stagnate. The manufacturing process can achieve this smooth geometry through modern forming techniques while maintaining ease of production.
Solution Approach 2:
The patent transforms the geometric parameters from a conventional conical design with sharp transitions to a bivariate normal distribution profile with optimized curvature parameters. This parameter optimization reduces flow resistance by ensuring smooth transitions throughout the funnel, eliminating harmful sharp edges while maintaining manufacturability through controlled geometric definition.
3Device complexity
If the funnel body uses simple conical geometry, then the device complexity is reduced, but the transport efficiency deteriorates due to poor flow guidance
Solution Approach 1:
The patent optimizes the geometric parameters by adopting a bivariate normal distribution shape, which provides mathematically defined optimal curvature transitions. This parameter optimization enhances flow guidance capability without significantly increasing device complexity. The bivariate normal distribution offers a balanced solution that improves transport efficiency while maintaining relatively simple funnel body geometry suitable for manufacturing.
Solution Approach 2:
The patent employs curved surface geometry based on bivariate normal distribution to improve flow guidance. The smooth curvature transitions naturally guide material flow through the funnel, enhancing transport efficiency without requiring complex internal structures or multiple components. The geometric complexity remains moderate while achieving superior flow characteristics.
Applied Scientific Principles
This section explains which scientific principles are used to turn an abstract innovation direction into a practical engineering solution.
Function Achieved in This Case
The bivariate normal distribution funnel effectively prevents blockages and enhances transport efficiency by minimizing fluid resistance, ensuring smooth flow and efficient discharge of substances.
Implementation Method 1
The funnel can be formed by rotating a normal distribution curve around the axis of symmetry z with a positive direction pointing to a deep part of the funnel, towards which a fluid in the funnel flows
Implementation Method 2
can be used for injecting liquid, powder, granules into a container with a small inlet or a pipe under gravity or certain forces
Data Source
AI summary
A funnel based on bivariate normal distribution is provided, and belongs to the field of daily tools. The funnel is formed by connecting a funnel body in a shape of a bivariate normal distribution with an outlet tube. The funnel body can be formed by rotating a normal distribution curve around the axis of symmetry z with a positive direction pointing to a deep part of the funnel, towards which the fluid flows. An outlet tube is a conical structure with a wide upper part and a narrow lower part. The surface of the funnel body has arbitrary order smoothness at everywhere. The design is simple and the fluid experiences little resistance when it flows through the inner surface. Thus, the funnel can effectively prevented blockage during the transport of fluid, powder and granules and the transport efficiency is remarkably improved.