Fluid mechanics-Total energy line of static system

In summary, the conversation is discussing the potential shape of the total energy line in a system with two reservoirs connected by two pipes, where the first reservoir is higher in elevation than the second. The question is whether the total energy line would be a straight line parallel to the ground or if it would slant down due to the difference in elevation and the slanting of the pipes. The Bernoulli equation is mentioned, and the possibility of the pressure having an effect is raised.
  • #1
5mmgridbok
3
0
I have two reservoirs, connected by two pipes. The first reservoir is higher in elevation than the second. If the system is full of static water, what would the total energy line look like?

Since the velocity of the flow through the system is 0, would the total energy line just be a straight line emerging from the water level of the higher reservoir and continuing parallel to the ground?
Or would it slant down due to the difference in elevation, following the slanting of the pipes? How would it end at the lower reservoir?

Thank you
 
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  • #2
You must show some work answering your own questions. PF is not a HW oracle.
 
  • #3
I'm sorry, I was trying to explain the extent of my reasoning in the second paragraph.
I will add more.

This is the Bernoulli equation:

z + (u^2/2g) + (P/pg) = Constant.
The velocity (u) being 0 simply follows on from my attempt at answering my own question.

Would the pressure have any effect?
 

1. What is the total energy line of a static system in fluid mechanics?

The total energy line of a static system in fluid mechanics is a graphical representation of the total energy at each point in the system. It shows the sum of the pressure head (static pressure), elevation head, and velocity head at a given point. This line is useful for analyzing the flow of fluids in a system and determining the potential for energy transfer.

2. How is the total energy line calculated?

The total energy line is calculated by adding the pressure head (P/ρg), elevation head (z), and velocity head (V^2/2g) at a given point, where P is the pressure, ρ is the density of the fluid, g is the gravitational constant, z is the elevation, and V is the velocity of the fluid at that point. The result is a line that represents the total energy at that point in the system.

3. What is the significance of the total energy line in fluid mechanics?

The total energy line is significant because it allows us to visualize the energy distribution within a static fluid system. It helps us understand how the different components of energy (pressure, elevation, and velocity) contribute to the overall energy at a given point. This information is crucial in designing efficient fluid systems and predicting the behavior of fluids in different scenarios.

4. How does the total energy line change in a flowing system?

In a flowing system, the total energy line will change as the fluid moves through the system. As the fluid flows, there may be changes in pressure, elevation, and velocity, which will affect the total energy at each point. The total energy line will shift and change shape to reflect these changes, and it can be used to analyze the energy transfer and efficiency of the system.

5. Can the total energy line be used to determine the direction of flow in a system?

Yes, the total energy line can be used to determine the direction of flow in a system. The flow will always occur in the direction of decreasing total energy. This means that the fluid will flow from points with higher total energy (such as a point with high pressure and low velocity) to points with lower total energy (such as a point with low pressure and high velocity).

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