Flow Through Pipes: Paraboloid Curve & Reason

In summary, the curve made by any liquid flowing through a pipe is in the shape of a paraboloid due to the velocity profile for laminar flow. This velocity profile can be calculated based on the distance from the center and shows that the velocity is maximum at the center of the pipe and zero at the corners due to friction at the walls. Understanding the calculation of the velocity profile can help explain this phenomenon.
  • #1
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when any liquid flows through a pipe, the curve made by it is paraboloid, what is the reason for this shape. also the equation tells that it is independent of the liquid flowing through the pipe
 
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  • #2
"the curve made by it"?
You mean the velocity profile for laminar flow?

You can calculate the velocity gradient as function of the distance to the center, and derive the velocity profile based on that. See the Wikipedia article, for example.
 
  • #3
i am talking about the velocity profile of the liquid, i know that from the equation it comes out to be a parabola equation, but what is its meaning, i mean why is it that velocity is maximum at the centre of the pipe and zero, at the corners?
 
  • #4
zero at the wall -> friction
increasing towards the center -> further away from the area of zero velocity, more flow

If you know how to calculate it, try to understand the calculation. I think it is quite intuitive to follow those steps.
 
  • #5


The reason for the paraboloid curve formed by liquid flowing through a pipe is due to the principles of fluid dynamics. When a liquid flows through a pipe, it experiences a pressure gradient, with higher pressure at the entrance of the pipe and lower pressure at the exit. This pressure gradient causes the liquid to accelerate and follow a curved path, which is described by the paraboloid curve.

The equation for the paraboloid curve is independent of the type of liquid flowing through the pipe because it is based on the physical properties of the pipe, such as its shape and size, and the pressure gradient applied to the liquid. Therefore, the shape of the curve will remain the same regardless of the type of liquid flowing through the pipe.

Understanding the flow of liquids through pipes is important in various industries, such as plumbing, chemical engineering, and oil and gas. The paraboloid curve is just one example of how fluid dynamics play a crucial role in the movement of liquids through pipes, and it is essential for scientists and engineers to understand these principles in order to design and optimize efficient pipe systems.
 

1. What is flow through pipes?

Flow through pipes refers to the movement of fluid or gas through a closed channel or tube. This can include water, oil, gas, or any other type of liquid or gas that can be transported through a pipe system.

2. What is a paraboloid curve in relation to flow through pipes?

A paraboloid curve is a mathematical shape that resembles a three-dimensional parabola. In flow through pipes, this curve represents the shape of the velocity profile of the fluid or gas as it moves through the pipe. It is often used to calculate the flow rate and pressure of the fluid or gas within the pipe.

3. How is the paraboloid curve related to the reason for flow through pipes?

The paraboloid curve is directly related to the reason for flow through pipes because it helps to determine the velocity and pressure of the fluid or gas as it moves through the pipe. This information is crucial for understanding the efficiency and effectiveness of the pipe system and its purpose.

4. What factors affect the paraboloid curve in flow through pipes?

The paraboloid curve in flow through pipes can be affected by several factors, including the diameter and roughness of the pipe, the viscosity and density of the fluid or gas, and the flow rate and velocity of the fluid or gas. Changes in any of these factors can alter the shape and characteristics of the paraboloid curve.

5. How is the knowledge of paraboloid curve and flow through pipes useful in real-world applications?

The knowledge of paraboloid curve and flow through pipes is essential in many real-world applications, including designing and optimizing plumbing systems, calculating flow rates in industrial processes, and predicting the behavior of fluids and gases in various engineering applications. It is also crucial for ensuring the safe and efficient transport of fluids and gases in pipelines for industries such as oil and gas, water supply, and wastewater management.

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