Calculating the speed of an airstream leaving a balloon

[emzy168]

Homework Statement

We can feel that as we blow up the balloon, the pressure inside it stays more or less constant; this is due to the elastic properties of the rubber sheet. Therefore, when released, the air will exit the balloon at a constant velocity. To test this idea, a round balloon was inflated with the aperture pinched shut between thumb and finger. Then air was let out in bursts by releasing the aperture, and the following data recorded for how the diameter varied with time:

Time (s) Circumference (cm)
0 72.5
1 65.5
2 57
3 44.5
4 30.5
4-5 minimum

Estimate the volumetric flowrate of the air leaving the balloon, and thus the average speed of the exiting air (assume the aperture has diameter 1 cm).
What is this speed on the Beaufort Scale, and is this reasonable?

Relevant Equations

Possibly Q = Av or some rate of change equation

I'm really not sure how to start this one!

 

[hutchphd]

Consider the first time interval of 1sec: how much air escaped?

 

[haruspex]

What is the relationship between circumference and volume?

 

[emzy168]

What is the relationship between circumference and volume?

Thanks for the reply!
If I can calculate the radius at each of the circumference values using:

Radius = circumference / (2*pi)

Then calculate the volume at each interval using:

Volume = (4/3) * (pi*r^3)

I can calculate the volume at each interval and thus the volume leaving at each interval.

Would the answer for each interval just be the volume per second so it’s a volumetric flowrate? And then I could average the values?

 

[emzy168]

Consider the first time interval of 1sec: how much air escaped?

Thank you!

 

[hutchphd]

I can calculate the volume at each interval and thus the volume leaving at each interval.

Would the answer for each interval just be the volume per second so it’s a volumetric flowrate? And then I could average the values?

Yes (although the last interval is suspect because the balloon collapses fully). From that number and the area of the neck opening you can get the speed.