2. Buoyancy Induced Lift Forces Flashcards
What is the lift on a balloon in a fluid
L = delta_rho *g * V (mass x acceleration)
What is the taut balloon assumption?
Volume of gas is constant, mass changes (hot air balloons)
What is the limp balloon assumption?
Mass of gas is constant, volume changes (weather balloons)
How does lift vary with height for a taut balloon under adiabatic conditions? (derive)
dL/dh = -1/(h_0* n) (Vg(ρ_a - ρ_b)
How does lift vary with height for a limp balloon under adiabatic conditions? (derive)
What assumption must be made for this question? (to do with n)
Assume that n is na for air and nb for balloon
dL/dh = [(Vg*ρ_a)/h_0] * (1/n_a - 1/n_b)
How would you find the change in height of a balloon given a change in a variable e.g. Temp?
delta h = dh/dt * delta T
What happens to a balloon’s dynamics during the day time?
The skin of the balloon is heated (hotter than surrounding air)
Therefore there is enhanced convection in order to convect the heat away
This enhanced convection removes energy and cools the gas within
Upward motion is diminished
What happens to a balloon’s dynamics during the night?
The skin of the balloon is colder than the surrounding air
Enhanced heat transfer heats gas within
Upward motion enhanced
What 3 things have an effect on the effective buoyancy/weight of the balloon
Gas volume
Ballast
Variation of balloon temp and air temp
What is the general process for deriving dL/dH under adiabatic conditions?
L = (ρ_a-ρ_b)gV
dL/dH = dL/dP * d/dP
find d/dp of the function of ρ using pv^n = C (adiabatic)
rearrange and use h0 = P/ρag
How would you find the effect of a change in temperature on the height of a taut or limp balloon at constant pressure?
Use ideal gas law to put replace the rhos in the lift equation with Ms and Ts.
then use:
ΔL = (dL/dTa) ΔTa + (dL/dTb) ΔTb
Explain the concept of virtual mass
virtual mass represents the mass of the balloon plus the mass of the air inside the balloon which must be dragged along with the balloon.
