In the eduction pipe of an air-lift pump the bubbles rise with greater velocity than the water owing to the slip due to their buoyancy. This seems to have no small effect on the action of the pump, and the present object is to construct formulae expressing the action of the slip in terms by which its effect can be determined separately from others. The writer on one occasion observed from accurate experiments that an air bubble noving up in still water attains its maximum velocity almost as soon as it has left the air nozzle and that then it rises almest uniformly with that maximum velocity. This shows that the velocity of slip of air bubbles in the eduction pipe of an air-lift pump is approximately constant all through its passage. With the metric system of measurements and in common logarithms, the equations for the lift, submergence, etc. are obtainea as follows : - L-{kηn23V logP}/Q, or V, Q=L/{23kηn log P} ; where V=nolume of air supplied at the atmospheric pressure in cub. m. per sec., Q=volume of water discharged in cub. m. per sec., L=lift in m., P=pressure of water expressed in atmospheres (absolute), which is roughly given by P=1/10S+1, S being the submergence in m., k=1-[2VQ(1-1/P)+V^2(1-1/P^2)+Q^2] Q/{46gA^2V logP}, A being the sectional area of the eduction pipe in sq. m., and g the accelerations of gravity=9.81 m. per sec. per sec., ηn=hydraulic efficiency, that is, the ratio of the actual lift to the theoretical one, and this involves various items such as the slip of air bubbles, hydraulic resistances in the pipe, and at the foot-piece, etc. The theoretical lift Lo is given by L_o=23VlogP/Q-VQ/gA^2(1-1/P)-V^2/2gA^2(1-1/P^2)-Q^2/2gA^2・The indicated efficiency ηn and the water horse-power N_w are respectively : ηn=QL/{23 VlogP}, and N_w=1000QL/75.
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