Fluid Mechanics of a weather balloon

In summary, the water supply of a building is fed through a main entrance pipe that is 6.0cm in diameter. A 2.0cm diameter faucet tap position 2.00m above the main pipe fills a 2.5x10^-2 m^3 container in 30.0s. The speed of the faucet and the gauge pressure in the main pipe are both .00083m^3/s.
  • #1
python023
12
0
Here are a couple problems I would like to check and a couple I'm not sure how to do:

1.3)A 650kg weather balloon is designed to lift a 4600kg package. What volume should the balloon have after being inflated with helium at 0C and 1 atm pressure to lift the total load?

Density of helium = .179 pa.
.179 = (650 + 4600)/Volume.
Volume = 29000m^3?

1.4) A submerged submarine alters its buoyancy so that it initially accelerates upward at 0.325m/s^2. What is the submarines average density at this time?

The density of seawater is 1.025x10^3 kg/m^3. From here I have no idea where to go. Can someone give me a hint?

2.2) Water is to be pumped to the top of the Empire State Building, which is 366m tall. What gauge pressure is needed in the water line at the base of the building to raise the water to this height?

Based on a formula from my book, Absolute pressure = atmospherice pressure + (density x free-fall acceleration x depth). So,
1.01x10^5 pa + (1.00x10^3 x 9.81 x 366) = 3.69x10^6 pa?

3.3) The water supply of a building is fed through a main entrance pipe that is 6.0cm in diameter. A 2.0cm diameter faucet tap position 2.00m above the main pipe fills a 2.5x10^-2 m^3 container in 30.0s. What is the speed of the faucet and What is the gauge pressure in the main pipe?

The cross-sectional area of the main pipe is .0113 meters^2. The cross-sectional area of the faucet tap is .0013m^2. The flow rate from the faucet is .00083m^3/s. From here I do not know where to go, can someone guide me in the right direction?

Thank you.
 
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  • #2
fluid mechanics reply

that's funny. i have the exact same problems in my textbook!
 
  • #3
Holt Physics 2002. You wouldn't happen to have the answers too? :smile:
 
  • #4
bump please
 
  • #5
bump again
 
  • #6
First, density can't be measured in pascals, which measures pressure.

You have to find ratios of the density of the fluid displaced vs the density of the fluid used, and when you multiply a density by volume you get either a force or mass, depending on whether you use mass or force density.
 
  • #7
The .179 pa on the first problem was a typo. So for the first problem i don't simply use density = mass/volume? I don't believe I know what the displacement will be do I? I only know the mass of the objects, the density of helium and the density of air. So how should I set up my equation?
 
  • #8
Draw a force diagram. You have the weight of the balloon and package directed down. You have the necessary Volume * (force density of air - force density of helium) as the bouyant force directed up.
 
  • #9
So, 5250 kg = (1.29kg/m3-.179kg/m3)V
Volume = 4700m^3
?
 
  • #10
Looks close, 4725 m^3, assuming your densities are correct. That would be about an 18 meter diameter balloon.
 
  • #11
Yes that's what I had before rounding to 2 significant digits, on 1.1. Thank you.
Any insight on 1.4 or 3.3?
 
Last edited:

1. How does a weather balloon stay afloat in the air?

A weather balloon stays afloat in the air due to the principle of buoyancy. The balloon is filled with helium, which is less dense than the surrounding air. This creates an upward force that counteracts the downward force of gravity, allowing the balloon to float.

2. What factors affect the motion of a weather balloon?

The motion of a weather balloon is affected by several factors, including wind speed and direction, temperature, pressure, and the weight of the payload attached to the balloon. These factors can impact the vertical and horizontal movement of the balloon.

3. How does a weather balloon collect data?

Weather balloons typically carry instruments called radiosondes, which collect data on temperature, pressure, humidity, and wind speed and direction as the balloon ascends through the atmosphere. The data is transmitted back to a receiving station on the ground.

4. What happens to the weather balloon after it reaches a certain altitude?

Once a weather balloon reaches a certain altitude, it will burst due to the decreasing air pressure. The payload attached to the balloon will then fall back to Earth via parachute, and the data collected will be transmitted back to a receiving station.

5. How is the shape of a weather balloon designed?

The shape of a weather balloon is designed to be as spherical as possible. This allows for the even distribution of helium gas inside the balloon, which helps to maintain its stability and prevent it from spinning or tumbling during its ascent.

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