Some questions on pressure drops and head loss in pipe flow

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

 

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

 

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.

 

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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
will read 100psi.

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.