to the ratio between the power and the cube of the quantity it Solving each of these formulas with respect to q:

circulates.

Hence, in any airway, for a constant pressure, the quantity

of air in circulation is proportional to the expression a'

a

ks

and for a constant power, the quantity is proportional to the

mine with respect to pressure and power, respectively; and their

q

q

values

and

are the potentials of the current with respect

to pressure and power, respectively. These factors evaluate the airway, as they determine the quantity of air a given pressure or power will circulate in that airway, in cubic feet per minute. By their use, the relative quantities of air any given pressure or power will circulate in different airways are readily determined. The rule may be stated as follows:

Rule. For any given pressure or power, the quantity of air in circulation is always proportional to the potential for pressure, or the potential for power, as the case may be.

This rule finds important application in splitting. In all cases where the potential is used as a ratio, the relative potential may be employed by omitting the factor k; or it may be employed to obtain the pressure and power, in several splits by multiplying the final result by k, as in the splitting formulas 46 and 47, page 275.

The accompanying table will illustrate the use of the formulas used in these calculations. There are several formulas for quantity, velocity, and work or horsepower, but in each case

the several formulas are derived by simple transposition of the

ksv2

terms of the original formulas p=

q=av, and u=qp.

a

To illustrate the use of the formulas, take an underground road, 5 ft. wide by 4 ft. high, and 2,000 ft. in length, and calculate the value of each symbol or letter, assuming a velocity of 500 ft. per min.

NOTE. The water gauge is calculated to 5 decimal places to enable all the other values to be accurately arrived at; in practice, it is only read to 1 decimal place.

*A horsepower is equal to 33,000 units of work.

†This coefficient of friction is an invariable quantity, and is the same in every calculation relating to the friction of air in mines.

As specimen calculations, take a formula for pressure and one Taking the values from the table and formula 7,

for quantity.

3

ksv2

น

for pressure and formula 20, q= Xa, gives

a

ks

In this way any of these formulas may be worked out.

Variation of Elements.-In the foregoing table, fixed conditions of motive column, as well as fixed conditions in the mine airways, were assumed. It is often convenient, however, to

know how the different elements, as velocity v, quantity q, pressure p, power u, etc., will vary in different circulations; as, by this means it is possible to compare the circulations in different airways, or the results obtained by applying different pressures and powers to the same airway. These laws of variation must always be applied with great care. For example, before it is possible to ascertain how the quantity in circulation will vary in different airways, it is necessary to know whether the pressure or the power is constant or the same for each airway. The following rules may always be applied:

For a constant velocity: q varies as a; p varies as as lo.

lo

;u varies

a

For a constant quantity: v varies inversely as a; p varies inversely as Xu3 (potential for power); u varies inversely as Xu (potential for power) or directly as p.

For the same airway:

The following terms vary as each other:

Similar Airways: r = length of similar side, or similar dimension.

For a constant pressure: U varies as ;q varies as r2

For a constant velocity: q varies as r2; p varies as -; u varies