[Conceptual Question] Fluid Mechanics Analysis of Pipe Flow

In summary, the question is whether the volume flow rate will change if the pipe network is shifted vertically by 10m while all other conditions remain the same. The relevant equations for calculating the elevation head of pipe flow are Hf = fL/d * V^2/g and Hl = KV^2/g. The answer is that the flow entrance distance below the free surface is the key factor in determining the flow rate, with the head being the driving force. While the position of the entrance may have a minor effect on the flow, the main factor is the head.
  • #1
aerograce
64
1

Homework Statement


As shown in the figure, if the pipe net work is shifted bodily by 10m vertically up the tank, and all the other conditions remain the same as the previous figure. Will the volume flow rate change?

Or I rephrase it as, in the calculation of elevation head of pipe flow, is the elevation head related to free surface height of the water in tank, or the entrance/exit position of the pipes from the tank?

Homework Equations


Relevant Equations are:
Hf=f L/d V^2/g
Hl= K V^2/g

The Attempt at a Solution


The attempt at this problem is:
I think it is related to free surface height of the water in tank only since in calculation we usually draw a line from one water tank free surface to another.
 

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  • #2
You are correct (if I understand you correctly). The flow entrance distance below the free surface is the key factor since it is this head that drives the flow. In the first figure, the entrance appears to be somewhat close to the tank bottom, and that could have a minor effect on the nature of the flow around the entrance, but the big factor is the head.
 

1. What is pipe flow in fluid mechanics?

Pipe flow refers to the movement of a fluid, such as water or gas, through a closed conduit or pipe. It is an important concept in fluid mechanics, as it is used to understand and analyze the behavior of fluids in various engineering applications.

2. How is pipe flow analyzed in fluid mechanics?

Pipe flow is typically analyzed using the principles of conservation of mass, momentum, and energy. This involves applying equations such as the Bernoulli's equation, the continuity equation, and the Navier-Stokes equations to determine the velocity, pressure, and other properties of the fluid within the pipe.

3. What factors affect pipe flow in fluid mechanics?

There are several factors that can affect pipe flow, including the diameter and length of the pipe, the viscosity of the fluid, the roughness of the pipe walls, and the velocity of the fluid. These factors can impact the flow rate, pressure drop, and other properties of the fluid within the pipe.

4. How does laminar flow differ from turbulent flow in pipe flow?

In laminar flow, the fluid moves in smooth, parallel layers with little to no mixing between them. This type of flow is characterized by low velocities and is typically observed in pipes with small diameters. In contrast, turbulent flow is characterized by chaotic, irregular movement of the fluid and is often observed in pipes with larger diameters and higher velocities.

5. What are the applications of pipe flow analysis in fluid mechanics?

Pipe flow analysis is used in a wide range of engineering applications, including the design of water supply and distribution systems, oil and gas pipelines, and HVAC systems. It is also important in understanding the behavior of blood flow in the human body and in the study of natural phenomena, such as river flow and ocean currents.

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