1844.] 



THE CIVIL ENGINEER AND ARCHITECT'S JOURNAL. 



441 



of the colder column will be equal to V (2-08 X 64) = 11-55 ft. per 

 second. 



The efflux of air under any given pressure can also be calculated 

 by the same means. For the pressure being known, it is only neces- 

 sary to calculate the height of a column of air which would be equal 

 in weight to this pressure. Thus if the pressure be equal to 1 in. of 

 mereurv, water is 827 times the weight of air, and mercury 13-5 times 

 the weight of water; therefore, 827 X 13-5 == 11 164 in. or 930-3 ft. ; 

 and according to the preceding formula V (930-3 X 64) = 244 ft. per 

 second for the velocity of efflux under this pressure of lin. of mer- 

 cury. 



In all these cases the velocity thus ascertained is independent of 

 any loss by friction. A certain deduction must be made for this loss, 

 wliic!) will vary greatly according to the nature and size of the tube 

 or shaft through which the air passes as well as with the velocity of 

 the air. Like all other fluids the retardation of the air by friction in 

 passing through straight tubes of any kind, will be directly as the 

 length of the tube and the square of the velocity; and inveriely as 

 the diameter. This question, however, becomes very complicated 

 under these circumstances, and particularly so when there are angular 

 turns in the tubes through which the air passes. The present state 

 of our knowledge on this subject does not allow of any very accurate 

 determination of the amount which ought to be deducted for friction 

 from the initial velocity obtained by calculation; and it is only by 

 empirical means we can arrive at an estimate of its amount. 



We shall proceed now to ascertain how far these theoretical calcu- 

 lations agree with the results obtained by experiments. 



In some new furnaces which Sir John Guest has lately added to his 

 extensive iron works at Dowlais, some experiments have been made 

 on the quantity of blast injected into the furnaces. In these experi- 

 ments, the machinery employed being new and of the best construc- 

 tion, the loss occasioned by the escape of air through imperfections 

 of the apparatus, was perhaps as small as possible. The engine for 

 blowing the furnaces made, at the time of the experiments, 18 double 

 strokes per minute. The diameter of the blowing cylinder was 100 

 inches, and the effective length of the stroke 7 ft. 6 in. From these 

 dimensions, therefore, it appears that 14726 cubic feet of air were 

 taken into the blowing cylinder per minute ; and the tubes through 

 which it was discharged from the receiver were six of 4 in. diameter, 

 and six of li in. diameter: the area of all these tubes was therefore 

 •5747 of a square font ; and the pressure of the blast measured by a 

 mercurial gauge was equal to 44 inches of mercury. Calculating by 

 the formula already given, we shall have V (827 X 13-58 X 4-5 -J- 

 12 X 64) = 519-2 ft., which is the velocity per second; and this 

 number multiplied by 60, and then by the area of the tubes, will give 

 519-2 X 60 X -5747 = 17903 cubic feet of air discharged per minute. 

 From this amount some deduction must be made for friction. The 

 velocity of the discharged air is 354 miles per hour; and with this 

 immense velocity, and through such small pipes the friction is no 

 doubt considerable. By deducting 18 per cent from the calculated 

 amount of 17903 cubic feet, we shall have 14G81 cubic feet, which 

 agrees within a fraction (namely 45 ft.) with the quantity obtainad by 

 measurement. 



In other experiments made at the same place, the followi*g were 

 the results. The quantity of air which entered the blowing cylinder 

 was the same as before, namely, 14726 cubic feet : the total area of 

 the tubes which discharged the blast was -5502 of a square foot, and 

 the pressure of the blast was equal to 4 in. of mercury. The calcu- 

 lation therefore, will be a/ (827 X 13-58 X 4 -f- 12 X 64) = 489-5 ft. 

 per second: and therefore 489-5 X 60 X -5502 = 16159 cubic feet 

 discharged per minute. The velocity of the blast in this case was 

 333 miles per hour; and if we deduct for friction 9 per cent from the 

 calculated amount, the remainder is exactly the quantity of air which 

 is ascertained by experiment to be discharged through the tubes. 



In a work published in 1634 by M. Dufrenoy, being a report to the 

 Director-General of Mines in France, on the* use of the hot blast in 

 the manufacture of iron in England, the results are given of many similar 

 experiments to the above; but with two exceptions the details are 

 not sufficiently ample to found any calculations upon. The two ex- 

 ceptions named are the furnaces at the Clyde and the Butterley iron 

 works, when they were blown with cold air. Both these blowing ma- 

 chines are described as having been in use for several years; and it is 

 therefore natural to suppose the various parts were more worn, and 

 fitted less accurately, than in those experiments already described. 

 The experiments were also made with less care. They show a dif- 

 ferent result to those already detailed ; as in these the calculated 

 quantity of air appears to be less than the quantity which entered 

 the blowing cylinders, in about the same proportion as it exceeded it 

 in the former cases. This difference no doubt arises from the imper- 

 fect fitting of the piston of the blowing cylinder, which by allowing 



a portion of air to escape, would diminish the apparent pressure on 

 the mercurial gauge, placed at the further extremity of the appar- 

 atus, and thence the calculated rate of efflux would of course be di- 

 minished. 



In the experiments at the Clyde works, the quantity of air which 

 was discharged into the furnace when estimated by the quantity that 

 entered the blowing cylinder, was 2827 cubic feet per minute. The 

 pressure of the blast was equal to 6 in. of mercury, and the area of the 

 tubes -0681 of a cubic foot. Calculating the discharge of air under 

 this pressure, it amounts to 2450 cubic feet, being 13 per cent less 

 than the measured amount, supposing no loss to occur by imperfect 

 fitting of the apparatus. 



At the Butterley works the quantity of air discharged into the fur- 

 nace, estimated by the contents of the cylinder, was 2500 cubic feet 

 per minute. The pressure of the blast was equal to 5 in. of mercury, 

 and the area of the tubes -0681 of a cubic foot. The quantity by 

 calculation appears to be 2235 cubic feet, being less by 10i per cent 

 than that shown by experiment. In both these last cases, however, 

 there is but little doubt that the loss of air from the cylinder caused 

 the pressure on the mercurial gauge to be less than it would have been 

 had the apparatus been perfectly tight ; and a very small diminution 

 in the observed height of the mercury would account for a much 

 greater difference in the velocity of efflux than is here shown. 



We are fully warranted in the conclusion, from these experiments, 

 that this method of calculation is as accurate as any theoretical de- 

 termination of such question can be; but from the results so obtained 

 an allowance must always be made for friction, which will necessarily 

 vary with the peculiar circumstances of each case. 



The following table will exhibit the results of the preceding ex- 

 periments at one view : — 



In order to show the results of the several modes of calculation 

 which different mathematicians have adopted, the following table has 

 been calculated from the data given in experiment Dowlais, No. 2, of 

 the preceding table, and it shows how far the several modes differ 

 from each other in their results: — 



Place of experiment, Dowlais. 



Pressure of blast in inches of mercury 



Area of tubes in square feet 



Quantity of air by experiment, in cubic feet 

 Quantity of air discharged (by calculation). 



Montgolfier 



Gregory 



Gilbert 



Sylvester 



Tredgold 



14726 



16159 

 15152 



14855 

 5017 

 15555 



•5502 



Considering the amount of friction which must result from the dis- 

 charge of air at the immense velocity which was obtained in this ex- 

 periment, namely, 333 miles per hour, and also that some of the tubes 

 were only li in. diameter, it will probably be considered that the 

 highest of these calculations is nearest the truth, as it only allows of 

 a deduction of 9 per cent being made for friction, to reduce the cal- 

 culated amount to the quantity obtained by experiment. It may 

 therefore be concluded that the method which gives this result, is the 

 most accurate as it is also the most simple for general use. 



60* 



