Pressure of air on coming to rest from various speeds Page: 4 of 7
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412 REPORT NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
The computations were made by various members of the aerodynamics staff in the Con-
struction and Repair Aerodynamical Laboratory of the United States Navy, and checked by
the aeronautics staff at the Bureau of Standards. The diagrams were made by Mr. F. A.
Louden.
The importance of the pressure excess due to compression may be judged from the tenth
column of the table. For speeds under 70 miles an hour the excess is less than Y per cent
of the impact pressure computed for air without compression. At 100 miles an hour, it is
0.41 per cent; at 150 miles, 0.96 per cent; at 300 miles, 4 per cent; at 800 miles, 31 per cent.
The last is about the speed of sound and of some propeller tips, while 300 miles is attained by
fast airplanes in diving.
VALIDITY OF FORMULA
The validity of (2) is here assumed without proof; viz, the compression is assumed to
occur without sensible heat transfer. At speeds above 150 miles an hour, for which the density
increment is no longer negligible, the compression of the air filament from Po to P2 may occur
in very brief time. To illustrate, suppose air streaming at 200 feet a second across a rod 1
inch in diameter. From both theory- and experiment one knows that the speed is sensibly
unchecked at points 1 foot before the rod and 1 foot behind it. Hence a particle traversing
this range must receive its maximum compression in about - second. The dissipation of
compression heat in this case may be assumed negligible, both because of suddenness and
because the heating or cooling of any filament is paralleled by that of its immediate neighbors,
thus lessening the temperature gradient.
It is commonly assumed also that for usual wind tunnel speeds the stop pressure on a
large body equals that on a like small one in like conditions. In 1902 the writer found the
impact pressure in the nozzle of a 1 -inch pitot the same as in.a pipe 5 inches in diameter when
both were pointed upstream in a 6-foot wind tunnel maintaining a steady 40-mile wind. (Ref-
erence 1.) In December, 1925, he found the impact pressure in a square-ended glass tube of
15-inch bore, pointed into a 40-mile wind, equal to that in a like tested neatly pointed hypo-
dermic tube 0.01 inch in diameter,2 truly to -as- inch of water.
Wid Os
FIG. 1.-Glass U-tube pointing upwind and held by spindle s of
aerodynamic balance. In a 40-mile wind, pressure in hypoder-
mic nozzle h balances that at b truly to rcj inch of water. Bore
of glass tube Y inch; bore of hypodermic tube 0.0097 inch
The arrangement for this latter test is shown in Figure 1. A glass U-tube of Y8-inch bore
with arms in a horizontal plane and pointing upstream, is held by a sheet metal clamp mounted
on the spindle of the aerodynamic balance in the 4-foot wind tunnel. With both ends wide
open in a 40-mile wind the U-tube was adjusted, by canting the balance, first till the small
piston of alcohol there shown just moved forward, then till it just moved backward. The
amount of cant was indicated by an Ames dial gauge at the tip of the balance beam. Now,
with the glass arms in their neutral position, and one plugged with a hypodermic needle of
T--inch bore, as shown, the piston rested in the same equilibrium position as before in the
same wind. Since the dial gauge showed that a cant of I in 10,000 is sufficient to move a
piston 3 inches long, of alcohol of specific gravity 0.81, the differential pressure between the
fine and coarse nozzle can not exceed about -doo inch of water.
For the medium speeds listed in Table I many experiments have shown that the pitot impact
pressure equals the reservoir pressure; that is, the pressure of stagnant air from which the stream
would issue with the speed Vo through a perfect nozzle. For such speeds therefore no corro-
borative data need be presented. For swifter flows Dr. Briggs furnishes some unpublished
measurements made by himself and Dr. Buckingham showing that the static air pressure in
a reservoir equals the pitot pressure in its fair discharge nozzle at exit speeds of 400 to 1,000
feet a second, but progressively exceeds it for higher speeds up to that of sound, though the
exess is but a few per cent. Check measurements with improved apparatus will be made by
them before publication.
2 Inside diameter 0.0097; outside, 0.0111 inch.
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Zahm, A. F. Pressure of air on coming to rest from various speeds, report, 1927; (https://digital.library.unt.edu/ark:/67531/metadc65899/m1/4/: accessed March 29, 2024), University of North Texas Libraries, UNT Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.