Flow thru a channel constriction

In summary: Your Name]In summary, when a part of the channel is constricted, the electric field becomes stronger due to the decrease in area. However, for the electric potential to remain constant, the distance between the plates must also decrease, resulting in an electric field equal to the one in case 1, Eo. Therefore, Emin = Eo in this scenario.
  • #1
fonseh
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Homework Statement


When a part of the channel is constricted , why will the Emin = Eo ?

Homework Equations

The Attempt at a Solution


I just have the figure showing in case 1 and case 2, Emin = Eo without any explanation ... Can someone explain about it ? I tried to search many online resource , but i get nothing .
 

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  • #2


Hi there,

When a channel is constricted, the electric field (E) becomes stronger due to the decrease in area (A) of the channel. This is because the electric field is inversely proportional to the area according to the equation E = V/d, where V is the potential difference and d is the distance between the plates.

In case 1, where the channel is not constricted, the electric field is weaker due to the larger area. In this case, the electric field is given by E = V/d1, where d1 is the distance between the plates in case 1.

In case 2, where the channel is constricted, the electric field is stronger due to the smaller area. However, in order for the electric potential (V) to remain constant, the distance between the plates (d2) must decrease as well. This is shown by the equation E = V/d2.

Since the potential difference (V) remains constant in both cases, we can equate the two equations and solve for E in terms of V, giving us E = V/d1 = V/d2. This means that in case 2, where the channel is constricted, the electric field is equal to the electric field in case 1, which is Eo. Therefore, Emin = Eo.

I hope this helps clarify the concept for you. Let me know if you have any further questions.


 

What is flow thru a channel constriction?

Flow thru a channel constriction is the movement of fluid through a narrow passage or channel. This can occur in natural environments, such as rivers or streams, or in engineered systems, such as pipelines or channels.

How does flow thru a channel constriction affect fluid dynamics?

Flow thru a channel constriction can greatly impact fluid dynamics. It can cause changes in velocity, pressure, and turbulence, leading to complex flow patterns. This can also affect the transport of sediments and other materials within the fluid.

What factors influence the flow rate in a channel constriction?

The flow rate in a channel constriction can be influenced by several factors, including the width and shape of the channel, the viscosity of the fluid, and the presence of any obstacles or roughness on the channel walls. Changes in these factors can affect the resistance to flow and therefore, the flow rate.

What are some applications of studying flow thru a channel constriction?

Understanding flow thru a channel constriction is important in various fields, such as civil and environmental engineering, hydrology, and fluid mechanics. It can help with the design and management of water systems, prediction of flood events, and optimization of industrial processes.

How is flow thru a channel constriction measured or calculated?

Flow thru a channel constriction can be measured or calculated using various methods, such as flow meters, velocity probes, or mathematical models. These methods take into account factors like fluid properties, channel geometry, and boundary conditions to determine the flow rate and other flow characteristics.

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