Page:Aerial Flight - Volume 1 - Aerodynamics - Frederick Lanchester - 1906.djvu/424

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App. II.

APPENDIX.

Now it by no means follows that the mean pressure throughout the region is the same as the mean pressure on the walls of the enclosure; in fact, we know from hydrodynamic principles that in many cases of fluid motion it is not so. In the case in point, however, it is manifest that the mean pressure is the same whether the integration is taken over the surface or throughout the volume, for (Fig. 160) the pressure on the walls of the box is point for point the same as for any surface parallel to these walls passing longitudinally through the region, and the pressure on the ends is of the same mean value, for the velocity of sound can be correctly computed on this basis.^[1] It is therefore evident that for a fluid obeying Boyle's law the existence of wave motion does not give rise to any change of pressure.

Under these circumstances it follows that change of pressure will take place in a region containing an ordinary gas ( $P/\rho ^{\gamma }=$ constant), the magnitude of which can be calculated from the energy of wave motion that passes into, and exists in, the thermodynamic system.^[2]

↑ See Addendum A.
↑ If heat be added to a quantity of a perfect gas contained within an enclosure, the consequent rise of pressure is due to the quantity of heat added and is independent of its distribution. "When wave motion exists in such a gas, heat is abstracted where the gas is rarefied and added where the gas is compressed, but more heat is added than subtracted; the difference represents the work done, according to well-known thermodynamic principles. We can therefore look upon the adiabatic wave as a Boyle's law wave in which heat has been added to one part and abstracted from another part, but in sum an addition of heat has been made to the contents of the enclosure, and the mean pressure increase can be calculated therefrom.
The fact that the distribution of added heat within a vessel does not affect the pressure increase has been taken advantage of by the author (1894) in the construction of an air calorimeter, a small quantity of gas whose calorific value is to be determined being burnt in a large vessel and the rise of pressure noted (see Addendum C). For mechanical reasons the appliance was not a success.
The result that the pressure due to an adiabatic wave can be deduced from the energy entering into the thermodynamic system appears to have been reached independently by Lord Rayleigh.

402

[1] See Addendum A.

[2] If heat be added to a quantity of a perfect gas contained within an enclosure, the consequent rise of pressure is due to the quantity of heat added and is independent of its distribution. "When wave motion exists in such a gas, heat is abstracted where the gas is rarefied and added where the gas is compressed, but more heat is added than subtracted; the difference represents the work done, according to well-known thermodynamic principles. We can therefore look upon the adiabatic wave as a Boyle's law wave in which heat has been added to one part and abstracted from another part, but in sum an addition of heat has been made to the contents of the enclosure, and the mean pressure increase can be calculated therefrom.
The fact that the distribution of added heat within a vessel does not affect the pressure increase has been taken advantage of by the author (1894) in the construction of an air calorimeter, a small quantity of gas whose calorific value is to be determined being burnt in a large vessel and the rise of pressure noted (see Addendum C). For mechanical reasons the appliance was not a success.
The result that the pressure due to an adiabatic wave can be deduced from the energy entering into the thermodynamic system appears to have been reached independently by Lord Rayleigh.

[1]

[2]