The Theory of the Pitot and Venturi Tubes, Part 2 Page: 1 of 10
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REPORT No. 2.
PART 2. o
THE THEORY OF THE PITOT AND VENTURI TUBES.
By E. BUCKINGHAM. 0
1. THE ENERGY EQUATION FOR STEADY ADIABATIC FLOW OF A FLUID.
Let a fluid be flowing steadily along a channel with impervious and
nonconducting walls, from a sectionA to a section A~, the areas of the 0 us
sections perpendicular to the direction of flow being also denoted by
A and A1. By saying that the flow is "steady" we do not mean that
it occurs in stream lines and without turbulence. We mean merely
that it is "sensibly" steady; i. e., that such variations of speed, 4
K direction of motion, pressure, etc., as may occur at any point in the -
stream as a result of turbulence are so rapid that our measuring instru-
ments do not respond to them, but indicate only time averages; and
that these time averages are constant at any fixed point within the
channel. Values of a property of the fluid, or of any other quantity
such as speed, "at a point," are therefore to be understood as time
averages over a time which is long compared with the speed of varia-
tion of the quantity to be measured, though it may appear short in
Sthe ordinary sense.
:era Let 0, p, v, e, T, respectively, be the absolute temperature, 'W
static pressure, specific volume internal energy per unit
S mass, and kinetic energy per unit mass, at the entrance sec- .
S tion A. By the "static pressure" is meant the pressure which would
be indicated by a gauge moving with the current. Let O, p, v, e1, gbm
T be the corresponding quantities at the exit section A Both sets.
of values are to be understood as averages over the whoYe section, as
well as time averages in the sense explained above. The two see- am
tions shall be at the same level, so that the passage of fluid from A
to A1 does not involve any gravitational work.
' As a unit mass of fluid crosses A, the work pv is done on it by the
fluid following; and as it crosses Ai it does the work pv1 on the fluid
ahead. Since the walls of the channel are nonconducting, no heat
enters or leaves the fluid between A and A1; hence the total energy,
internal plus kinetic, increases (or decreases) by an amount equal to
the work done on (or by) the fluid, and we have
pv-pV1= (e + T)- (E,+ T)
T- T, = (eg +pmw) - (e+pv)
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Buckingham, E. The Theory of the Pitot and Venturi Tubes, Part 2, report, January 1, 1989; (digital.library.unt.edu/ark:/67531/metadc53589/m1/1/: accessed August 18, 2017), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.