**Determination
of coefficient of friction**.

__Objective:__

To determine the Darcy-Weisbach resistance coefficient and coefficient of friction for the (PVC) ducting system for the mine ventilation laboratory from the measurement of frictional pressure loss and to compare it with theoretically calculated value for smooth ducts.

__Introduction:__

For
an incompressible flow in a mine airway the frictional pressure loss, DP, over a certain length L, is given by:

** ****D****P = fl**

** 2D A ^{3}
**

f = Darcy-Weisbach resistance
coefficient (dimensionless)

L = length of airway (m)

U = average velocity of airflow,
m/s.

r= Air density (kg/m^{3})

D = equivalent diameter of airway, m

A = airway cross-sectional area, m^{2}

P = perimeter of the airway, m

K = coefficient of friction = fr/8 Ns^{2}/m^{4}

S = rubbing surface = P * L, m^{2}

Q = quantity flow rate, m^{3}/s.

The Darcy-Weisbach resistance
coefficient is a function of the airway surface roughness, and the flow regime,
given by the Reynolds number, (Re).

However, in practice, the density of
air does not vary much in a mine and the flow in most cases can be considered
turbulent enough for the value of ‘f’ to remain constant irrespective of
Reynolds number of flow . Thus, the coefficient of friction K is essentially
considered to vary with the surface roughness.

Based on the Reynolds number and the
surface roughness, the value of ‘f’ is either read from the charts or computed
empirically. For a smooth pipe flow (absence of surface roughness) two such
empirical relationships exist.

Blasius Equation**: f = 0.316/(1/4) (2000< Re< 100000)**

Karman-Prandtl Equation: **f ^{1/2} = [2 log (Re * f^{1/2})
– 0.8] -------(for Re> 100,000)**

The Reynolds number is given by Re =
vD/n, where v is the average air velocity (m/s),
D is the equivalent diameter (m), and n is the kinematic viscosity
(m^{2}/s). For the average ambient temperature n may be taken to be 1.6 * 10^{-5} m^{2}/s.

__Instruments:__

Experimental
duct setup, Askania minimeter, inclined tube manometer, scale and calipers,
Assmann Psychrometer, and Aneroid barometer.

__Procedure: __

(1)
Fully
throttle the split on the experimental setup containing the bend.

(2)
Level
the inclined tube manometer and the Askania minimeter.

(3)
Connect
the Askania to the two static portals on the main split between which
frictional pressure loss is to be measured and take the initial reading

(4)
Connect
the inclined tube manometer to the venturimeter orifice plate on the main split
and take the initial reading.

(5)
Measure
the length of the duct over which Askania/manometer is connected as well as the
inner diameter of the duct.

(6)
With
the fan running obtain the static pressure drop from the Askania/manometer and
the venturimeter/orifice plate reading from the inclined tube manometer.

(7)
By
regulating the throttling on the main split, obtain 5 to 6 sets of Askania and
venturimeter readings.

(8)
Measure
the ambient temperature and the barometric pressure values to obtain a
representative air density during experimentation.

__Computations:__

Using
the inclined tube calibration chart and the Venturimeter calibration chart,
convert the w.g. values from the inclined tube manometer to obtain quantity
flow rates (Q) in the duct. Plot the graph between P (frictional pressure loss)
values versus (SQ^{2}/A^{3}) values. The frictional pressure
loss values are the one obtained from Askania, converted to Pascal. The slope
of the straight line fitted through points gives a measure for the coefficient
of friction.

By considering the average value of
1.6 * 10^{-5} m^{2}/s, compute the Reynolds number. From these
and the empirical equations given above, compute the Darcy-Weibach coefficient
of friction for all the flow conditions generated. Taking into account the air
density, determine the corresponding ‘coefficient of friction’ values. Compare
these values with the one obtained from the graph.

__Remarks:__

(1)
The
frictional pressure values tend to be just a few Pascal in the experiment.
Caution must be exercised in reading the Askania observations accurately.

(2)
The
Karman-Prandtl equation used to measure the Darcy-Weisbach coefficient of
resistance is different from the one given above under the known surface
roughness conditions.

(3)
Density
of the sir inside the duct would be slightly different from that of the air
entering the duct, depending on the pressure and temperature of air in the
duct.

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