Journal of electricity, power, and gas . G C the effective head =BC = h the water quantity B E = Q; the total headG B = H. It will then be seen that when h is coincides with G and EB = Q = O. When Q is max. E coincides with F and BC = Oand GC = GB = f. Now the energy is proportional tothe area BCDE and this area is greatest when GC = 354 JOURNAL OF ELECTRICITY, POWER AND GAS [Vol. XXXII_No. 17 CB or the greatest energy is obtained when 1/3 of 2 the head is expended in friction. This is howeververy seldom the most economical point at which towork the pipe line. To sacrifice 1/3 of the ene
Journal of electricity, power, and gas . G C the effective head =BC = h the water quantity B E = Q; the total headG B = H. It will then be seen that when h is coincides with G and EB = Q = O. When Q is max. E coincides with F and BC = Oand GC = GB = f. Now the energy is proportional tothe area BCDE and this area is greatest when GC = 354 JOURNAL OF ELECTRICITY, POWER AND GAS [Vol. XXXII_No. 17 CB or the greatest energy is obtained when 1/3 of 2 the head is expended in friction. This is howeververy seldom the most economical point at which towork the pipe line. To sacrifice 1/3 of the energy re-coverable from any water fall for the purpose of aslight saving in the first cost of the pipe is a graveerror. For example, if a pipe line would cost $10,000delivered at the power site and develop 10,000 per cent loss, it would be better to designthe pipe for only 5 per cent loss and we may thenobtain 10,000 + per cent or 2830 additionalby the extra expense of a larger pipe. It is obvious t-t^h ?~rzr~ n. Fig. 39. that to avail ourselves of this and with the same Q( in the above table) we must now have a fric-tion loss of 5, or to put it in another way we mustwith a slope or friction loss of 5 be able to force Q = through the new pipe where a $10,000 pipe wouldcarry Q = on a slope of From formula (39)v=CVsr it is seen that in the first 1 case Vs= and v- and we may C\/r d2 for approximate comparison assume C to be constantthen for the same quantity of water. Const Const = V r\/s and— — = yn Vs. (40) d: d. and d2 X Vr X = X Vr> X But r dV= Vs» . •. d/» = Vs. and = ? *-d2 4d.(41) d 5 or = 1 and = = d. The weight of the new pipe will be increased inproportion to the diameter and to the thickness butthe thickness ^ as the diameter hence the weight and(therefore very closely the cost) varies as the (diam- eter)2 hence our new pipe will weigh and cost ab
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