"These formulas comprise the pressure due to resistance, and not that necessary for final velocity: they are, therefore, more correct for long than for short airways. The pressure required for final velocity becomes a smaller fraction of the whole drag as the airways extend. If it be required to take into account the pressure to create velocity, Instead of using pa = ksv2, use a(p – P) = ksv2. Instead of using p ksv a P= Instead of using s = pa, use (PP) κυ Instead of using v = pa (P - P)a 124 MINE VENTILATION. $45. APPENDIX B. PROBLEMS. 45. 1. What is the area of an airway 6 feet by 5 feet? What is its perimeter? a = 30; o = 22. Ans. 2. What is the area of a shaft 14 feet diameter? 153.98 + feet. Ans. 8. What is the perimeter of a shaft 16.5 feet diameter? Rule. - Diameter X 3.1416. 58.83+ feet. Ans. 4. The long axis of an elliptical shaft is 14 feet, its short axis 6 feet: what is its area? Rule. - AX a × 0.7854. 65.9736 feet. Ans. 5. Find the perimeter of an elliptical shaft whose axis A is 16 feet, and its axis a 8 feet. 6. An air-course is 500 yards long, 6 feet high, and 7 feet wide: what is its area, perimeter, and rubbingsurface? a = 42; 0 = 26; s = 39000 square feet. Ans. 7. What is the rubbing-surface of a shaft 15 feet diameter, 1,200 feet deep? 56548.8 feet. Ans. 8. In an airway 8 feet by 9 feet, when the current has a velocity of 15 feet per second, what quantity of air is passing per minute? Rule. - a × υ Χ 60". 64800 cubic feet. Ans. 9. When the water-gauge is 1.85 of an inch, what pressure per square foot does it indicate? Rule. w × 5.2. 9.62 pounds. Ans. 10. When the quantity of air passing is 60,000 cubic feet, with a water-gauge of 1.5 inches, what are the units of work producing ventilation? Rule. - u = pq. 468000 units. Ans. 11. What horse-power is there in 468,000 units of 13. There are 50,000 cubic feet of air passing, having a rubbing-surface 24,000 feet, and an area of 20 square feet: what is the water-gauge ? ksv2 a 3.12 inches water-gauge. Ans. 126 MINE VENTILATION. § 45. 14. The rubbing-surface of an airway is 25,000 feet, its area 25 square feet: what is its length ? 1250 feet. Ans. 15. What units of work are necessary to overcome friction of an airway 6 feet by 6 feet, 1,000 feet long, when the quantity passing is 7,200 feet per minute? Rule.u= ksv2 a X q. 4166 units. Ans. 16. Let a = 36; 8 = 24,000, to find the value of 17. With 0.9 of an inch water-gauge, 16,000 cubic feet of air are passing: what quantity will pass when there is a water-gauge of 1.6 inches? √0.9:√1.6:: 16000:21333+. Ans. 18. With a fan and furnace combined, 46,706 cubic feet are produced; the furnace produces alone 42,670 cubic feet: what will the fan produce by itself? √467062-426702 = 18993. Ans. 19. If, with a water-gauge of 0.65 of an inch, 20,000 cubic feet of air are obtained, what height will the water-gauge be when there is a quantity of 75,000 cubic feet of air passing? 1 x. x X w = 9.139. Ans. 91 20. How much must we increase the pressure to double the quantity of air? 4 times. Ans. 21. How much has the ventilating power to be increased to treble the quantity of air? 3327 times. Ans. 22. If we obtain 25,000 cubic feet of air by 5-horse power, what horse-power will be required to circulate 60,000 cubic feet in the same mine? (q'): (q)3 :: 5HP: Ans. or q:q:: V5: VAns. 23. There are two air-courses through which a total quantity of 100,000 cubic feet of air is passing; the resistances of the airways are in the proportion of 4 to 1: what quantity will pass along each? VI × 100000 √4 + VI 100000 3 = 33333 cubic feet for airway having greater resistance. = 666663 cubic feet for airway having √ + VI only one-fourth the resistance. √4 × 100000 24. Find the motive-column where the upcast and downcast shafts are 540 feet deep, the temperature of the upcast being 129°, and that of the downcast 43°. 129-43 Rule. - M = D × 459 +43 92.51. Ans. |