Equivalent Orifice.-If an opening be cut in a thin plate and the latter be then placed at right-angles to the direction of air in motion so that the air in its passage is obstructed by the plate, it meets with resistance in passing through the opening. M. Murgue assimilates the workings of a mine to such an opening in calculations for ventilating purposes, which he calls the equivalent orifice. To find the equivalent orifice for any given mine:—

A =

k =

Quantity of air in cubic feet per second passing through the opening (ie. circulating round the mine).

Ventilating pressure in feet of air column, required to overcome the resistance of the mine.

contracta

Opening in thin plate in square feet (i.e. equivalent orifice).
Co-efficient of contraction of orifice (ie. vena
= '65).

Q = √2 ghax kA = √2 ghax 65 A.

Then :

It is however often more convenient to use the following units, viz. :— thousands of cubic feet per minute; ha in inches of water-gauge.

Q in

The average value of A for English mines is said to be about 20 and for Belgian 86 square feet.

Orifice of Passage.-The air in being exhausted from a mine meets with obstruction at the ventilator, the effect of which is to reduce the duty of the ventilator. The observed depression produced by the ventilator is always higher than where ascertained in the roadways of approach, the increase being to some extent due to overcoming the various resistances in the ventilator. M. Murgue treats this as the orifice of passage.

As to the volume of the ventilative current required for any particular colliery, this will depend entirely upon its own circumstances. The volume of air inhaled by a man is 27.8 cubic feet per hour. Smyth, in his Coal and Coal Mining, says: "In round numbers 100 cubic feet of air per minute may be required for the health and comfort of each person underground, or for 100 men 10,000 cubic feet; but if fire-damp be given off at, say, the rate of 200 cubic feet per minute, we should need at the very least 30 times that amount of fresh air to dilute it, or 6,000 cubic feet in addition. Increase the number of men and liability to gas

and 40,000 or 60,000 cubic feet of air may be indispensable for safety." In André's Mining Engineering there is a definite formula for finding the ventilative current necessary in a mine as follows:

V = m 24+ h 72 + p 192 +ƒ (9 × 2,700 + s),

where V = Ventilative current in cubic feet a minute. m = The number of persons employed.

h = The number of horses in the mine.

=

The weight in pounds of the gunpowder consumed an hour as a maximum.

ƒ = A factor of safety which would vary in different districts as well as in different mines, so as to be 2, 3, 4, 5, or more times: this can only be determined by the judgment of the engineer, but it must not be taken at less than 2 under the most favourable circumstances of a mine worked by longwall (post and stall requiring more) and yielding very little firedamp.

9 = The output or average quantity of coal raised a minute in tons. and s The exposed surface of the coal in square yards, which can be calculated from the output and the thickness of the seam. A horse is assumed to breathe 6 times the quantity of air required by a man, and to require 3 times the quantity required by a man and his lamp.

Applying this rule to a mine worked by longwall, in which say 400 tons per day of 8 hours are raised, 200 men employed underground and 10 horses, and 10 lbs. of gunpowder per hour are used, the extent of coal surface exposed being 600 square yards, we have V = (200 × 24) + (10 × 72) + (10 × 192) X 2,700 + 600

+ 2

ة)

400

8 × 60

500).

Then V = 13,140, that is taking f, the factor of safety, at its lowest figure and assuming the mine to be fairly free of gas, but if it be fiery and the factor 5 be adopted, the quantity would be 21,690 cubic feet.

If Smyth's rule be applied to this example

For the men 200 x 100 = 20,000

may be necessary for the gas, which is not definitely known.

CHAPTER XII.

THE FRICTION OF AIR IN MINES: VENTILATION.

*

The Pressure necessary to Overcome Friction-Rate of Increase or Decrease of Pressure-Power necessary to produce Ventilation-Rate of Increase or Decrease of Power--Best Form of Airway-The Co-Efficient of Friction-Measurement of Ventilating Pressure-Loss of Pressure in Shafts and Airways-Splitting the Air into an Upper and a Lower CoalseamDimensions of Ventilating Fans-Splitting the Air in Three Coalseams-Splitting in One Coalseam in Communication with more than Two Shafts-The Effect of Obstructions and of Regulators in Airways-Bratticing-Natural Ventilating Pressure-Examples on Pressures and Powers of Different Shaped Airways-Questions and Answers on Ventilation. THE friction of air in mines arises from its rubbing along the top, bottom and sides of the aircourses in its course round the workings. It is not difficult to understand that the more rubbing surface there is presented to the air, the more friction there will be, and that the amount of rubbing surface depends upon the length and perimeter of the road along which the air is taken. It is also obvious that the faster the air is made to travel, the more will be the friction. The late Mr. Atkinson has most ably argued the theory of circulating the air in mines, and he says in his Practical Treatise on the General Principles of Ventilation, that “ the pressure required to overcome the friction of air increases and decreases in exactly the same proportion that the area or extent of the rubbing surface exposed to the air increases or decreases, so that when the velocity of the air and the sectional area of the airway remain the same, the pressure required to overcome the friction is proportional to the area or extent of the rubbing surface exposed to it; and hence if we double or treble the extent of the rubbing surface, we also double or treble the friction, or what is the same, the force or pressure required to overcome it." Again he says "the pressure required to overcome the friction in the same airways varies in the same proportions that the square of the velocity of the air increases or decreases, so that a double velocity of air in the same airway meets with a double double or fourfold resistance, a treble velocity meets with a treble treble or ninefold resistance; and a velocity of four times as great gives rise to a resistance four times four or sixteen times as great. In the same way a half velocity meets with one half of a half or 4th of the resistance; 3rd of the velocity encounters only a third of a third or 4th of the friction, and so on." "It seems probable that for every foot of rubbing surface and for a velocity in the air of 1,000 feet per minute, the friction is equal to 0.26881 feet of air column of the same density as the flowing air, which is equal to a pressure, with air at 32°, of 00217 lb. per square foot of area of section. Calling this the co-efficient of friction, we have the following rules with respect to the friction of air in mines :

where

pressure per square foot.

a = square feet of sectional area.

s = the area of rubbing surface exposed to the air.

v = the velocity of the air in thousands of feet per minute, 1,000 feet per minute being taken as the unit of velocity.

k the co-efficient of friction in the same terms or unit as pis taken in."

"The quantity of air only varies as the cube root of the power, and of the quantity of coals burnt to produce it; so that eight times the coals only double, and twenty-seven times the coals only treble the quantity of air circulating in a mine, whether the ventilation is produced by furnace action, ventilating machines, or otherwise, so long as the airways remain in the same unaltered state."

It may be learned from these quotations that theoretically airways should be as smooth and as free from obstructions as possible, because roughness and inequality such as would be caused by projecting pieces of rock or timber, or from falls in aircourses, produce friction. Again, theoretically, the best form of aircourse is the circular, because a circle whose area is 1 square yard has a perimeter equal to 3'545 yards, whereas a square whose area is 1 square yard has a perimeter of 4 yards. The square form is preferable to the rectangular, for a rectangular airway 6 feet by 1 feet has an area of 1 square yard, but its perimeter is 2 + 2 + 1 + 1/ 5 yards. It is not convenient to have circular airways in mines, so the square form should be adopted as far as practicable; also theoretically, large airways are preferable to a number of small ones representing the same area.

=

THE CO-EFFICIENT OF FRICTION.

The late inspector of mines for the South Durham district, Mr. J. J. Atkinson, fixed the value of the co-efficient of friction in the galleries of a coal mine at 000417. In other words, a depression measured by o'00417 inch of water is required to propel air at a velocity of 1,000 feet per minute through a gallery whose rubbing surface is one square foot. This is equivalent to a pressure of 00217 lb. per square foot. Valuable experiments to determine the value of the co-efficient have been made by others, with different results. M. Daniel Murgue, a very able authority on questions of mine-ventilation, made a series of careful experiments upon short lengths of airways, with the object of ascertaining the value of this co-efficient for three well-defined classes of airways, viz., galleries unsupported, galleries lined with masonry, and galleries propped with timber. In these experiments M. Murgue used a delicate form of water-gauge, the readings upon which could be observed, by means of a microscope, to o'0008 inch. In straight galleries, with unsupported sides, four experiments were made, three of which were in normal or large cross-measure drifts. The mean value of the co-efficient of the loss of pressure in the three airways was equal to o'00095. The fourth experiment was made in a rising gallery of small area, and a greater air velocity was produced. Here the co-efficient was 000123. In galleries lined with masonry, five experiments were made. Of these, two were made in normal straight airways of regular outline, the mean value of the co-efficient of the loss of pressure being o'c0033. One experiment was made in a normal gallery having a long continuous curve, almost a semicircle (see Fig. 639), but the air measurement was

made in the straight portion preceding the curve. Here the value of the co-efficient of the loss of pressure increased to 0'00062, so that the projection of the current of air against the concave side of the unbroken curve had the effect of nearly doubling the friction in the straight gallery. Two other experiments were made in galleries, one of intermediate, and one of small area, which, although sinuous, had a general straight direction (see Fig. 640). In the larger of these, the mean value of the co-efficient of friction was o'00052, and in the smaller, which was only 22.9 square feet area, the co-efficient increased to 0'00055. Three experiments were made in timbered galleries, two of which were in normal airways, having the usual sinuosities of galleries driven in the seam and not set out by marks, one being an old gallery, and the other a newly-repaired one. The mean

Fig. 639.-ILLUSTRATING THE EFFECT OF A CURVE IN INCREASING THE CO-EFFICIENT OF THE
LOSS OF PRESSURE.

value of the co-efficient of friction obtained was o'00158. A final experiment was made in a gallery of small area, the curvatures in the airway being greater than in the preceding cases, and the surface irregularities between the props relatively of greater importance. In this instance the co-efficient of friction reached the highest point obtained, viz., O'00241.

From these experiments it is plain that the values of the co-efficient of friction are not only different in different types of galleries, but are influenced by curves in the airways, the sectional area, and their inclination. In galleries of small area, for each of the three types, there is an increase in the co-efficient of friction.

It will be seen then, that there is difficulty in fixing a mean value for the co-efficient of friction for the whole of the galleries in a mine. In conducting

Fig. 640.-ORDINARY SINUOSITIES IN A MINE GALLERY.

any experiment upon the friction of air in mine galleries, there is great difficulty in obtaining an adequate length of gallery possessing a continuous regularity of area and uniformity of outline. Results obtained from experiments in short sections of airways probably differ from those made in long ones, where the presence of refuge holes, stenton ends, and other openings interrupt the regularity of air-flow and increase the amount of resistance. However desirable it may be to have a correct co-efficient of friction for air-currents, it is not possible to fix one which can be applicable to all mines, but that of 0'00417 inch of watergauge adopted by the late Mr. J. J. Atkinson, has hitherto been generally accepted. It has therefore been thought advisable to base all calculations which appear in this work, on these figures; if they are wrong, the error is on the safe side, and this is of importance when considering the friction of the mine, with a view to the erection of a ventilating fan.