as in a stream with rigid boundaries.
| Fig. 8. |
In the case of compressible fluids the variation of volume due to the difference of pressure at the two sections must be taken into account. If the motion is steady the weight of fluid between two cross sections of a stream must remain constant. Hence the weight flowing in must be the same as the weight flowing out. Let p1, p2 be the pressures, v1, v2 the velocities, G1, G2 the weight per cubic foot of fluid, at cross sections of a stream of areas A1, A2. The volumes of inflow and outflow are
A1v1 and A2v2,
and, if the weights of these are the same,
G1A1v1 = G2A2v2;
and hence, from (5a) § 9, if the temperature is constant,
p1A1v1 = p2A2v2.
(3)