# What does resistance of a fluid flow depend on?

May 27, 2018

see below

#### Explanation:

the resistences to the flow of a fluid can be continuous or localized.
Continuous resistence are due by the viscosity of the same fluid, by the rugosity of the pipe, by the geometry of pipe, and by the velocity of the fluid in the pipe.

one possible relationship is:
$R = f \times \frac{L + {L}_{e q}}{d} \times {v}^{2} / 2 g$
where
-L is the lenght of the pipe,
-d is its diameter,
-Leq is the equivalent Lenght, a factor that considers all the obstacles to the movement as curves, narrowings, enlargements, valves (opened or partially closed) and so on.
-v is the velocity
-g is the gravity acceleration (so R is in meters)

viscosity is hidden in the friction coefficient f that is determined in function of Reynolds adimensional number (Re) according with the attached Moody's diagram
$R e = \frac{d \times \rho \times v}{\mu}$
Where:
d is the diameter
$\rho$ the fluid density
$\mu$ the fluid viscosity
v the velocity