Do Not Fear the Friction Factor!

Background: this is the second step to my fluid flow experiment recorded in the blog "Neosynephrine". Any likeness of this experiment to the "Crazy Fluid Experiment" on MySpace is totally coincidental.

Objective:
To verify the relationship between pressure drop and flow rate which is presented in the literature (BSL) as the dimensionless friction factor-- Reynolds Number correlation. In a way that confirms this correlation with data taken in the laminar, transition, and turbulent regimes. So that we can present these relationships in an alternative form useful for particular design applications!

Precautions:
1. Wear safety goggles or glasses!

2. Check manometers or gauges for balance each time the meter is connected to the process!!

3. Do not disconnect any manometer or gauge while the process is under pressure!!!

4. Report any loss of mercury to the Chief!!!!

5. Do not start flow when valves are set in such a way that mercury manometers or gauges will be imbalanced or have mercury blow out of the meter!!!!!

Derivation:
Fk = A.K.f, f = friction factor
A = characteristic area, for full tubes = (2R.pi.L) [=] m^2
K = characteristic kinetic energy/ volume = ((1/2).rho.v^2) [=] J/m^3

substituting into first equation-

Fk = (2.pi.RL) ((1/2).rho.v^2).f [force] = [Newtons]
usually - &P is measured, not Fk, hence

Fk = (-&P).pi.R^2 [=] Pa. m^2 [=] N and from a force balance:
(2R.pi.L) ((1/2).rho.v^2) f = (-&P).pi.R^2 comes that:

f =(-&P).pi.R^2/(2.pi.RL) ((1/2).rho.v^2), after simplifying:

f = (1/4) (d/L) (&P)/((1/2).rho.v^2) and d=2R

f = f(Re), as Re = d.v.rho/mu

Data:
---------------------------------------------------------------------------
q (liters/sec.) v1 (cm/sec.) v2 (cm/sec.) A1 (cm^2) A2 (cm^2) f1 f2
-------------------------------------------------------------------------------------------------
0.034---------- 26.8--------- 47.7---------- 1.27-------- 0.713-- 0.1860 0.0220

0.00775------- 9.86--------- 27.4---------- .7854-------.2827-- 0.0700 0.0108

0.044---------- 62.4--------- 22.5---------- .7125------ 1.979---0.0026 0.0290
--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------

Woody out.