roswell

dz
Cit
v
27800
Aa
=
:
ascent velocity of balloon (ft./sec.)
volume of gas lost per foot of ascent (ft.3jrt.)
area of appendix opening (rt.2)
The back pressure caused by this velooity~
(9)
or,
(10)
~p =
.6p =
v =
dg =
dao =
14.7 =
1333 =
( 2 dg
v ) . 14.7 -dao1333
back pressure induced ~psi)
velocity of escape of gas (ft./sec.)
density of lHting gas at altitude
of balloon (lb./ft.3)
density of air at see level (lb./ft.3)
pressure of air at sea level (psi)
escape velocity of air to produce back pressure
of 1 atmosphere at sea level ( ft I sec)
combining equation ( 8) ar.d ( 9):
( di! V I )I
dt .27800 ·ra-.6p : -
(1333 14.7 ddg
Go
psi
As an example, let us find the back pressure induced in a 20'
diameter balloon with a 1' diameter opening ascending at
800 ft./minute, as it becOMes full at 30,000 ft·. (density of
helium @ 30 ,ooo ft. = £511· fll-. O.l3 8 dao )
Ap,. J 'If·,!'~~~ ..;r)" · 14.7 • o.Olll:. 2 75x 1 o·~psi
It is to be noted that equation (5) can be e.rrived at by ;nore
sirrple reconstruction of the ste.ndard equation for fluid flow:
(11) ~~ = Cd Aa -/2gh
-ff = · volume rate of flovr. (ft. 3/sec.)
cd = a constant of flow