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Aviation History
1931
1931 - 1037.PDF
SEPTEMBER 25, 1931 69 THE AIRCRAFT ENGINEER SUPPLEMENT TOFLIGHT (4) There JS no intermolecular attraction. (This is not an hypothesis of the kinetic theory of gases, but is assumed in this elementary theory.) (5) The average value of the speed of the molecules is constant at constant temperature, the action of heat being to increase the velocity of the molecules. (Speed of translation.) (6) There is no energy lost in rotation of the mole- cules. Consider the cube side I, containing N molecules of ga.^ at ordinary pressure. Resolve the velocities parallel to ED, DC and AD. Then we can say that on the average one-third of the molecules will be travelling parallel to each direction, and work on this assumption; but we will not make this assumption. Suppose a molecule whose velocity perpendicular to the face AC is x, rebound from it, then the change in momentum = 2mx. After the rebound the molecule will move towards the 21opposite face FH, and after a time—, it will collide X with the face AC again. Therefore in one second it will make — impacts with the face AC. This is the same, of course, for the face FH. If there are N molecules in the cube, then the change in momentum is: — 2 mx X X N = Nm - per sec. the same force will be exerted on the face FH. Similar reasoning gives results for the y and z directions. Hence xl Vs z% 2 Km - + 2 KM - + 2 Nw - = I 61* p. where p is the pressure. The above follows since force = change in momentum per sec. 2 NOT I ) •'•* Nwi "V1) = = x* +V2 also since m is the mass of a molecule, N the number. NOTN»I is the mass of the volume Is of gas. Hence -^j- = p the density. ••• i P ~yS = P- or -v3p now p = 14.7 x g IDS. per sq. in. p = 0.0764 lb. per cu. ft. 3 X 14-7 x 144 x 32-3 = 1665 ft. per sec. 0-0764 The velocity of sound is 1,120 ft. per sec. velocity of molecules•'• — = 1-486 approx. velocity of sound This is due to the fact that the molecules are not infinitely small, and therefore it takes time for the momentum, to be passed on when two molecules collide, oenuc the velocity of sound is less than the velocity of the ndividual molecules. -ft must bo remembered that the velocity V is the rootmea i square velocity of the molecules, and this is not ^ece«ariry equal to the average value of the velocities of he ; adividual molecules. The two averages are only "e >'me if all the velocities of the molecules are the same, or nearly so. In a gas there are so many wilis.onS) ^.na^ j£ one n10iecuie) say; is travelling faster tnan the rest., it will collide with molecules, and the extra velocity it has will be quickly dissipated among the rest. From viscosity considerations the number of collisions a hydrogen molecule makes per second at 0 deg. C. and the atmosphere pressure is 1.17 X 1010. For air the number is still enormous. From the value of V obtained it follows that if we could pull a plane through the air at 1,665 ft. per sec, the air would be left behind, and a vacuum formed. The resistance would be increased, therefore, enor- mously, in fact, on the elementary theory just worked out, the pressure would be 4^ atmospheres, i.e. 4.5 x 14.7 x 144 = 9,540 1b. This is not actually the pressure, as further energy would be used in forming eddies and sound waves. An ordinary motor cycle would, therefore, be unable to exceed this speed, no matter how great its horse- power, when stationary and engine full on, since the air inlet on the carburettor on motor cycles is facing to the rear, and hence, since the motor cycle would be travelling faster than the air could overtake it, no air would be drawn into the carburettor to form an explo- sivp mixture. The horse-power would, therefore, virtually become zero, although from stationary con- siderations infinite. FROM "AERONAUTICS IN THEORY AND EXPERIMENT" v . VELOCITY OF" PROJECTILE VELOCITY OFSOUND This would be true for an aeroplane, if the car- burettor was the same; but, further, a vacuum tends to form behind the airscrew, and therefore it cannot get any purchase on the air. The problem is not, however, so simple as this, as an airscrew consists of a variable aerofoil moving along a helicoidal path, and the air does not impinge perpendicularly. However, the effici- ency of the aerofoil elements would be very poor at these velocities, and terrible eddies and vortices would be formed in their trail. Sound waves would also be pro- duced. The resistance of most well-shaped bodies varies as the square of the speed. The graph shows the varia- tion in the resistance coefficient of a projectile with V increase of —. The resistance coefficient is constant up v r to 500 ft. per see., therefore the resistance is accurately proportional to the square of the speed. Beyond this velocity, the resistance coefficient rapidly increases up to a point greater than the velocity of sound. It then settles down to a constant value after having decreased. The maximum value of the resistance coefficient corre- sponds to the velocity of the molecules, but there are other factors coming in. At these velocities, the air would be compressed, the pressure and density therefore970 e
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