# A Treatise on Physics. Vol.1

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This historic book may have numerous typos and missing text. Purchasers can usually download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1901 edition. Excerpt: ...is therefore qp, and this must be the same at every point in a stream-line. If then a be the area of a tube and M be the rate of flow of fluid across a section, we have a = MJqp. Since M is constant the value of a will be least where qp is greatest. Now we have for a maximum or minimum of qp or 9--1 df dp p dp' and therefore qdqldp =-1 /p. Substituting in the value of dqjdp just found we obtain cUjjdp =-jqp =-qfp.dpjdp, or dp/dp=ljqthat is dp or the velocity is that of the propagation of sound. When this is the case the cross-section of the stream is a minimum, for clearly this must give a maximum value of q p. Now in the case of adiabatic flow by (48) q-= '2(1'-P)/(y--1); Pig. 186. Po 1Kb hence, since for maximum flow along a stream-line we have q-= V-= 2 Va'/(y + 1) or p/p =pjp0.2j(y + 1). This last result, with p/p? =Polp? gives e_ / 2 v=i p /__ y--Po r+y ' Po y+1' or if y = 141, p = '635p0, and p = '527p0. The conclusion is that if pv the pressure in the receiving chamber, be less than this, the stream, after coming to a minimum width, widens again somewhat, as shown in Fig. 186. The curve drawn normally across the streams from A to B is evidently concave outwards, and therefore the narrowest parts of the tubes must be on the outward side of that curve, as indicated by the cross-lines. The pressure in the narrowest part of each stream-tube cannot be less than m527pt, nor p lass than-ti35p0. Outside this the streams must widen and the velocity increase since p diminishes. If, however, the pressure jo, outside the orifice be greater than this the flow will be in parallel tubes at the narrowest part and the pressure will be pt. When the velocity of flow is greater than J no disturbance of pressure can be propagated back along the...