The figure given shows the forces exerted on a hot air balloon system. Formulate the drag force as
FD-AC
where pair density (kg/m³), v velocity (m/s). A projected frontal area (m²), and Cd the dimensionless drag
coefficient (0.47 for a sphere). Note also that the total mass of the balloon consists of two components
m-ma+mp
where mg the mass of the gas inside the expanded balloon (kg) and mp the mass of the payload (basket, passengers,
and the unexpanded balloon 265 kg). Assume that the ideal gas low holds (P= PRT), that the balloon is a perfect sphere
with a diameter of 17.3 m, and that the heated air inside the envelope is at roughly the same pressure as the outside air.
The parameters are: Normal atmospheric pressure P= 101,300 Pa, the gas constant for dry air R=287 joules/kg-K, the air
inside the balloon is heated to an average temperature 7-100 °C, and the normal (ambient) air density p 1.2 kg/m³
NOTE: This is a multi-part question. Once an answer is submitted, you will be unable to return to this part.
Fo
Forces on a hot air balloon: Fg buoyancy, FG weight of gas, Fp weight of payload (including the balloon envelope).
and FD drag. Note that the direction of
the drag is downward when the balloon is rising.
Use Euler's method and Excel to compute the velocity from 10 to 60 s with Ar-2s, given the previous parameters along with the
initial condition, v(0) 0 (m)
The values of velocity from 0 to 60 s are as follows
r(s)
0
2
4
8
28
42
00
v (m/s)
0