Fluid dynamics in horizontal pipe

In summary, the conversation discusses a scenario involving a large cylinder labeled "reservoir" and a small vertical cylinder labeled "column 1", connected by a horizontal pipe. When a more viscous liquid is substituted for a less viscous one, the fluid velocity at point B decreases but the fluid height in column 1 remains unchanged. The conversation also touches on the application of Bernoulli's equation in this scenario and why it is not generally applicable to viscous flows.
  • #1
Bengo
46
0
There's a figure that comes with the question but I'm having trouble attaching it so I will describe it the best I can.

There is a large cylinder labeled the reservoir. A horizontal pipe is connected near the base of the reservoir and it is open at the other end so fluid flows out (point B). Then a small vertical horizontal cylinder labeled column 1 that is connected at about halfway of the horizontal pipe.

What will be observed when a more viscous liquid, of the same mass density, is substituted for the less viscous liquid in the system?

Answer: a lower fluid velocity at point B, but an unchanged fluid height in column 1.

I've found 2 threads on this question on another site but I still don't understand how the height of column 1 remains unchanged if the fluid velocity is slower. Wouldn't that mean increased pressure meaning the fluid in column 1 will rise?

Thank you!
 
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  • #2
What causes the slower velocity?
 
  • #3
Increased viscosity?
 
  • #4
Yes, but what specifically slows it down?
 
  • #5
Flow rate? According to poiseuilles principle?
 
  • #7
I don't think anything is changing other than the viscosity and the flow rate. The pressure difference is the same, so is the length and radius.
 
  • #8
Alright, so if the pressure difference is the same, what does that say about the pressure along the horizontal pipe and therefore the height of the column in the attached vertical tube?
 
  • #9
Oooh I think see now. So if there was another column closer to the reservoir the height would be higher compared to the original column? But I still don't understand why Bernoullis equation doesn't apply. That's what I originally used, thinking decreased speed --> higher pressure
 
  • #10
Well first, Bernoulli's equation doesn't apply to viscous flows, which this clearly is. There are certain corrections that you can make to empirically apply it to things like pipe flow, but you can't do it straight up and you can't do it at all analytically.

Second, Bernoulli's equation doesn't generally apply to comparing points in two different flows originating in different reservoirs because it is really a statement of conservation of energy. So with two different reservoirs, the total energy isn't guaranteed to be the same in the two situations and therefore Bernoulli's equation is not necessarily meaningful. This is related to why it doesn't work for viscous flows since viscosity is dissipative and is going to break this sort of energy balance equation. Now, it just so happens that in this situation, since you held all the other parameters constant, if there was no viscosity, using Bernoulli's equation would have worked, but that result is not general and you shouldn't get into that habit.
 
  • #11
Wow it's so much clearer now. Thank you so much!
 

1. What is fluid dynamics in horizontal pipe?

Fluid dynamics in horizontal pipe is the study of how fluids, such as liquids or gases, flow through a pipe in a horizontal direction. It involves understanding the behavior of the fluid, including its velocity, pressure, and energy, as it moves through the pipe.

2. How does the diameter of the pipe affect fluid dynamics?

The diameter of the pipe has a significant impact on fluid dynamics. A larger diameter pipe will allow for a higher flow rate and lower pressure drop, while a smaller diameter pipe will have a lower flow rate and higher pressure drop. The diameter also affects the velocity of the fluid, with a larger diameter resulting in a lower velocity and a smaller diameter resulting in a higher velocity.

3. What is the relationship between fluid viscosity and fluid dynamics?

Fluid viscosity, or the resistance of a fluid to flow, plays a crucial role in fluid dynamics. High viscosity fluids, such as honey, will have a lower flow rate and higher pressure drop compared to low viscosity fluids, like water. Viscosity also affects the velocity of the fluid, with high viscosity fluids having a lower velocity and low viscosity fluids having a higher velocity.

4. How is pressure affected by fluid dynamics in horizontal pipe?

Fluid dynamics in horizontal pipe has a significant impact on pressure. The pressure at any point in the pipe is determined by the fluid's velocity, density, and viscosity. As the fluid moves through the pipe, the pressure will change due to factors such as friction and changes in velocity.

5. What are some applications of fluid dynamics in horizontal pipe?

Understanding fluid dynamics in horizontal pipe has many practical applications, such as in the design and operation of pipelines, irrigation systems, and HVAC systems. It is also crucial in industries such as oil and gas, chemical processing, and water treatment, where the efficient and safe transport of fluids is essential.

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