# Some questions on pressure drops and head loss in pipe flow

I would like to ask you that why pressure drop is constant through pipe? How can we know that dP/dx=constant?

Thank you.

Chestermiller
Mentor
If it's an incompressible fluid, how does the fluid know that the conditions in one part of the pipe are different from another part of the pipe? The average fluid velocity is the same everywhere.

If it's an incompressible fluid, how does the fluid know that the conditions in one part of the pipe are different from another part of the pipe?

I cannot work out your answer. Both sentences. What do you want to mean by "If it's an incompressible fluid, how does the fluid know that the conditions in one part of the pipe are different from another part of the pipe? What condition? I am asking about how the formula 8.19 appeared or is derived?

The average fluid velocity is the same everywhere.

What is the relation between the pressure drop and average fluid velocity you have mentioned?

Thank you.

Chestermiller
Mentor
If the fluid velocity is constant throughout the pipe, then everything else about the flow must also be constant, including the axial pressure gradient. What other possibility is there?

If the fluid velocity is constant throughout the pipe, then everything else about the flow must also be constant, including the axial pressure gradient. What other possibility is there?

I do not know what other possibility is but I want to study it. Under what topics of fluid mechanics, can I find this situation. And would you like to explain with what equation or from where do we know that if fluid velocity is constant then all other things should be constant. This means that all other things only the function of velocity as well.

So, I will study more but I need guidance.

Thank you.

Gold Member
What is your existing background in fluid mechanics? Have you ever taken a course in the subject?

What is your existing background in fluid mechanics? Have you ever taken a course in the subject?

Yes I have taken a course, I try to make a refresh these days. But as you see, I stick in some parts of the topics. But I try to understand those part by asking.

Thank you.

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Chestermiller
Mentor
I do not know what other possibility is but I want to study it. Under what topics of fluid mechanics, can I find this situation. And would you like to explain with what equation or from where do we know that if fluid velocity is constant then all other things should be constant. This means that all other things only the function of velocity as well.

So, I will study more but I need guidance.

Thank you.
Try reading the first few chapters of Transport Phenomena by Bird, Stewart, and Lightfoot.

The equation posted is the definition of pressure loss over the length at a given velocity.. (Initial pressure-final pressure)/length...

Chestermiller
Mentor
The equation posted is the definition of pressure loss over the length at a given velocity.. (Initial pressure-final pressure)/length...
What if the substance is a gas (axially varying velocity) or if the temperature is varying axially (axially varying viscosity). The the pressure gradient is not constant for these situations. Do you still maintain that this is the definition of the the pressure loss?

I'd say so... the formula given doesn't account for any variation of other parameters...
If you wanted a formula to include different flow rates, viscosities, pressures, compressability, etc it would get complicated really quickly..

As presented, at a given pressure, flow, and viscosity, you can find the pressure drop per unit length.

Chestermiller
Mentor
I'd say so... the formula given doesn't account for any variation of other parameters...
If you wanted a formula to include different flow rates, viscosities, pressures, compressability, etc it would get complicated really quickly..

As presented, at a given pressure, flow, and viscosity, you can find the pressure drop per unit length.
I agree. But it's certainly not a definition.

Rx7man
JBA
Gold Member
deleted post

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why pressure drop is constant through pipe? How can we know that dP/dx=constant?
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if a pressure gauge located at one end of a pipe reads 100psi then that
does not say that a pressure gauge located anywhere else along the pipe

any fluid traveling through a pipe will meet pipe resistance from the walls of the pipe.

the formula is used to determine the size of pipe that you need to use in order to
lessen the amount of pressure drop between inlet and outlet of the pipe.

an example of using a larger pipe for instance
will allow for a lesser pressure drop at the outlet side
of the pipe.
you want to use a water pump to deliver 5000 gpm
across a distance of 1 mile and still have 43 psi water pressure.
so if your using a water pump that has a 5000 gpm output @ 100psi
but your 1 mile long pipe only has a 1 square inch inside cross section
then the resistance to fluid flow would be so great that the pressure drop
that occurs between the inlet and outlet sides of the pipe would call
for a design change of pipe size in order to attain the 5000 gpm flow rate
at the desired 43 psi water pressure.

as long as you have a large enough pipe diameter and the water will
not need to be elevated then you can retain most if not all of the pressure
over the 1 mile pipe run but larger pipes cost a lot more money than smaller pipes
or water pumps with a higher pressure and gpm output.

in fact if there is enough of a downgrade where the pipe is installed then you will end up
with a higher pressure than the original 100 psi due to the force of gravity pulling the entire
contents of water in the pipe downwards.

to carry that a little further even if the 1 mile long pipe is level you can retain the 100 psi
pressure and the 5000 gpm flow rate if a large enough pipe is used due to the force of
gravity acting on the water in the pipe.

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If it's an incompressible fluid, how does the fluid know that the conditions in one part of the pipe are different from another part of the pipe? The average fluid velocity is the same everywhere.

This post is very hard to understand. What is the relation between being imcompressible fluid and fluid know the conditions in parts of the pipe? What's if average fluid velocity is the same everywhere?

Thank you.