If, however, only some point e is reached at the cross-section S min, the pressure increases in the widening part of the nozzle, corresponding to a return down the curve from e towards c. At the outer end of the tube j takes a definite value, j 1, max= j * S min/ S 1, and the pressure has the corresponding value, denoted in Fig. 56), the pressure continues to diminish in the widening part of the nozzle, while j begins to decrease also, corresponding to the segment ba of the curve. If the maximum flux density is reached at the cross-section S min(the point b in Fig. 56 shows j as a function † of p, and the variation just described corresponds to the interval from c to b. In the narrowing part of the nozzle, the flux density increases (and the pressure falls) the curve in Fig. The maximum flux density j *, if reached, can again occur only at the narrowest cross-section, so that the discharge cannot exceed S min j *. If we consider only the flow in the immediate neighbourhood of the end of the tube, the motion of the gas after leaving the tube is essentially flow round an angle, the vertex of which is the edge of the tube mouth we shall discuss this flow in detail in §104. Thus the gas cannot acquire a supersonic velocity in flowing through a nozzle of this kind. The velocity at the end of the tube and the discharge also remain constant for p e< p *. For air ( p * = 0.53 p 0), the maximum pressure drop is 0.47 p 0. In other words, the pressure drop along the tube cannot be greater than from p 0 to p *, whatever the external pressure. When the external pressure decreases further, the pressure p 1 remains constant at p *, and the fall of pressure from p * to p e occurs outside the tube, in the surrounding medium. For p e= p * the velocity becomes equal to the local velocity of sound, and the discharge reaches the value Q max. The velocity υ 1 with which the gas leaves the tube, and the total discharge Q= j 1 S min, increase monotonically, however. When this pressure decreases from p 0, the pressure inside the vessel, to the pressure p 1 at the outer end of the tube decreases also, and the two pressures p 1 and p e remain equal that is, the whole of the pressure drop from p 0 to p e occurs in the nozzle. ![]() Let us now follow the change in the manner of outflow of the gas when the external pressure p e diminishes.
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