Compressed air; theory and computations . hen air is mixed with water as in these pumps, it may beassumed to act under isothermal conditions. Then the energyin the air is pava logc r while the effective work realized by waterdelivered at top of discharge pipe is s2s being the velocity of discharge. Write ^— = hi. Then if E be the efficiency of the pump (reckoned from energy in air deliv-ered) we have the equation wQ (h+h,) = Epava log„ tu _ w(h + h) . Q Epaloge r {6V In case of a pure-water air-lift pump w = , and we may take for average atmospheric conditions pa = 2,100. Then mul
Compressed air; theory and computations . hen air is mixed with water as in these pumps, it may beassumed to act under isothermal conditions. Then the energyin the air is pava logc r while the effective work realized by waterdelivered at top of discharge pipe is s2s being the velocity of discharge. Write ^— = hi. Then if E be the efficiency of the pump (reckoned from energy in air deliv-ered) we have the equation wQ (h+h,) = Epava log„ tu _ w(h + h) . Q Epaloge r {6V In case of a pure-water air-lift pump w = , and we may take for average atmospheric conditions pa = 2,100. Then multiplying by and using common logarithms the formula becomes •p j. v h + hi . For pure water ^ - 77^5^ (35) Complete data on several apparently well-designed air-liftpumps with ratio of submergence between 50 and 65 per cent,and total submergence between 350 and 500 ft. show E to have avalue between 45 and 50 per cent, (see Art. 43). If we take E = 45 per cent., Eq. (35) becomes va h + hi Q 35 logib r (36) THE AIR-LIFT PUMP 81. CO 04 Plate IV. 82 COMPRESSED AIR Formula (36) is recommended for the design of deep-wellpumps. In this hi may be taken as about 6 ft. which is assum-ing a discharge velocity between 20 and 25 ft. For shallow wellshi may be taken as 1, which would correspond to a velocity of8 ft. The curves on Plate IV represent Eq. (36) for ratios of sub-mergence as shown thereon. Note that in Plate IV an efficiencyof 45 per cent, is assumed. When more data have been collected,some modification may be found desirable. In any case some excess air capacity should be provided; forshould the free water surface in the well drop more than antici-pated, after prolonged pumping, more air will be needed tomaintain the discharge. This is apparent on Plate IV. Note that as submergence ratio S decreases -£ increases. Velocity in the Water Pipe.—This is the factor that most affectsthe. efficiency, but unfortunately, owing to the usual small area inthe well, the velocity
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