Hydraulics help please -- Energy loss in a long pipeline

In summary: For constant diameter pipes, velocity will vary with head loss. In summary, the conversation discusses the use of an equation to calculate energy loss in a pipe system. The equation includes variables such as pressure, velocity, and height. The participants in the conversation also discuss assumptions made in using the equation, such as the pressure at the top being equal to zero and the velocity heads being equal. They also mention the use of the continuity equation and the Darcy and Heinz-Williams equations to solve for a particular problem.
  • #1
fayan77
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0

Homework Statement



Screen Shot 2018-10-04 at 7.43.51 PM.png

Homework Equations


y1 + P1/##\gamma##+v1/2g=y2 + P2/##\gamma##+v2/2g+hL

The Attempt at a Solution


I used the above equation and assumed that P1=0 and both velocity heads are equal. Is that valid? However I did not need to use the geometry of the pipe so I think I am doing something wrong. Can someone point me in the right direction?
 

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  • #2
I think you are right, the pipe is uniform, but since the problem asked for energy loss, you must derive (from the energy conservation equation) a correct equation that has some kind of energy loss. In the end it must be some kind of power loss ##P=\frac {dW} {dt}##.
Sorry I loss my mind for a moment, yes it's the loss per feet.
 
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  • #3
Im looking for energy loss in terms of feet not power loss. I have a lot of information
Pressure
heights
flow rate
length
diameter
no roughness
what is throwing me off is that if I use general energy equation are my assumptions correct that P1=0 and that velocity heads are eqaual?
If i use darcy weisbach eq. i do not have temperature or roughness to help me determine friction factor
 
  • #4
I think P1 is 1atm, not 0 like you assumed, this pressure (P1) only equal zero if the head is placed in vacuum, or the inlet pressure is the reference pressure. In the first case the water would be boiled off to vacuum and then this question would be invalid. In the second case I believe they must first say that the reference is at that point (the inlet). They just say the pressure at the outlet is 18psi so that mean it is the absolute pressure (reference to vacuum) and that the inlet pressure is at normal condition of 1atm. For the velocity I think they are equal.
 
  • #5
What is the definition of "energy head?"
 
  • #6
potential energy of a static column of water (height) + velocity head + pressure head... the equation I have written above
 
  • #7
The give you the energy head at point 1 and they give you everything you need to calculate the energy head at point 2. The difference is the energy loss (head).
 
  • #8
So my assumptions are correct? velocity heads are the same and that pressure at the top = 0? And while I have you here, does Darcy's equation and Heinz-Williams yield the same loss? can I use them in combination to solve for a particular problem?
 
  • #9
fayan77 said:
So my assumptions are correct? velocity heads are the same and that pressure at the top = 0? And while I have you here, does Darcy's equation and Heinz-Williams yield the same loss? can I use them in combination to solve for a particular problem?
None of this is right. We have $$y_1+\frac{p_1}{\gamma}+\frac{v_1^2}{2g}=80\ ft$$From the information provided in the problem statement, what are ##y_2##, ##\frac{P_2}{\gamma}##, and ##\frac{v_2^2}{2g}##?
 
  • #10
y2 = 12
P2/##\gamma## = 18*144/62.4 =41.5
velocity head @ section 2 = (Q/A)2/64.4 = .14

solving for hL = 80 - 12 - 41.5 - .14 = 26.36 ft

why is P1 = 0? and why is velocity head @ section 1 = 0?
 
  • #11
fayan77 said:
y2 = 12
P2/##\gamma## = 18*144/62.4 =41.5
velocity head @ section 2 = (Q/A)2/64.4 = .14

solving for hL = 80 - 12 - 41.5 - .14 = 26.36 ft
Correct
why is P1 = 0? and why is velocity head @ section 1 = 0?
Who says?[/QUOTE]
 
  • #12
OOOOOHHHH I see, problem states energy head for section 1 as a whole is 80 ft I was fixated that 80ft was y1... got it

Thank you.

On another note whenever I am solving a problem with a two reservoir system we assume velocity heads are zero because of their size the dh/dt is basically 0 correct? So if I have a system with only one reservoir i will have an equation like so, Energy head section 1 = velocity head + hL can I use continuity equation to solve for velocity or will velocity vary with head loss?
 
  • #13
fayan77 said:
OOOOOHHHH I see, problem states energy head for section 1 as a whole is 80 ft I was fixated that 80ft was y1... got it

Thank you.

On another note whenever I am solving a problem with a two reservoir system we assume velocity heads are zero because of their size the dh/dt is basically 0 correct? So if I have a system with only one reservoir i will have an equation like so, Energy head section 1 = velocity head + hL can I use continuity equation to solve for velocity or will velocity vary with head loss?
For any reservoir, dh/dt is usually small.
 
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1. What is energy loss in a long pipeline?

Energy loss in a long pipeline refers to the decrease in pressure and flow rate of a fluid as it travels through the pipeline. This is caused by various factors such as friction, changes in elevation, and bends in the pipeline.

2. How does friction affect energy loss in a long pipeline?

Friction between the fluid and the walls of the pipeline causes energy to be converted into heat, resulting in a decrease in pressure and flow rate. This is known as frictional head loss and is dependent on the fluid velocity and the roughness of the pipeline walls.

3. What is the significance of changes in elevation in energy loss?

Changes in elevation, such as an increase or decrease in the pipeline's height, can lead to energy loss in a long pipeline. When the fluid moves to a higher elevation, it gains potential energy and loses kinetic energy, resulting in a decrease in pressure and flow rate. The opposite occurs when the fluid moves to a lower elevation.

4. How do bends in a pipeline affect energy loss?

Bends in a pipeline cause the fluid to change direction, resulting in a loss of kinetic energy and an increase in pressure. The sharper the bend, the greater the energy loss. This is known as bend or curvature head loss.

5. What are some ways to reduce energy loss in a long pipeline?

There are several ways to reduce energy loss in a long pipeline, including using larger diameter pipes to decrease friction, minimizing changes in elevation, and using smoother pipeline materials to reduce friction. Additionally, installing straightening vanes or flow control devices at bends can help reduce energy loss. Regular maintenance and proper design of the pipeline can also help minimize energy loss.

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