Calculating Hot Air Balloon Volume & Lift

Thread starter Desperate
Start date Apr 23, 2021
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Air Balloon Constant speed Hot Lift Temperature Volume

In summary, the volume of a hot air balloon can be calculated by multiplying the balloon's radius squared by pi (π) and then multiplying that by the height of the balloon. The lift capacity of a hot air balloon is dependent on several factors, including the size of the balloon, the temperature of the air inside the balloon, and the weight of the basket, passengers, and fuel. The lift of a hot air balloon is directly affected by the temperature of the air inside the balloon, with hot air producing more lift than cold air. The maximum altitude a hot air balloon can reach depends on various factors, with specialized balloons being able to reach heights of 20,000 feet or more. The lift of a hot air balloon is affected by

Apr 23, 2021

Desperate

Homework Statement: We have to make a hot air balloon that can rise up to 5km and bring up 4 people. In total, the balloon weight is 750 kilogrammes. We cannot exceed the temperature of the air inside by 100 degrees C. We have to find how the temperature of air must change in order for the balloon to maintain a constant rising speed.

Relevant Equations: Fl = V (ρc - ρh) ag

Volume of hot air ballon
V=((4/3 pi R^3)/2) + (1/3 pi h (R^2 + r^2 + Rh) = 2956.24 m3

Balloon:
R=9m
h=15m
r=1m

m = 750 kg
H = 5000m
T = 373 K
p1 = 101300 Pa
p2 = 50650 Pa
M(air) = 0.029 kg/mol
F = mg - 7350 N

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Apr 23, 2021

phinds

Science Advisor

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You need to show more of an attempt at working this out. Also, "We cannot exceed the temperature of the air inside by 100 degrees C" is an ambiguous statement. Please clarify.

FAQ: Calculating Hot Air Balloon Volume & Lift

How is the volume of a hot air balloon calculated?

The volume of a hot air balloon is calculated by using the formula V = (4/3)πr³, where V is the volume and r is the radius of the balloon.

What factors affect the volume and lift of a hot air balloon?

The volume and lift of a hot air balloon are affected by several factors, including the temperature of the air inside the balloon, the temperature of the surrounding air, the weight of the balloon and its contents, and the altitude at which the balloon is flying.

How does the temperature of the air inside the balloon affect its lift?

The temperature of the air inside the balloon affects its lift because hot air is less dense than cold air. When the air inside the balloon is heated, it becomes less dense and therefore, lighter than the surrounding air. This creates a buoyant force that lifts the balloon.

Why is it important to calculate the lift of a hot air balloon?

Calculating the lift of a hot air balloon is important because it helps determine the maximum weight that the balloon can carry. This is crucial for safety reasons and to ensure that the balloon can fly properly without any issues.

Can the volume and lift of a hot air balloon be adjusted during flight?

Yes, the volume and lift of a hot air balloon can be adjusted during flight by controlling the temperature of the air inside the balloon. By adding or releasing hot air, the volume and lift of the balloon can be increased or decreased, allowing the pilot to control the altitude and direction of the balloon.