The kids and I were watching an episode of Mickey Mouse Clubhouse the other day, and I found myself wondering how many helium-filled balloons it would take to get Daisy Duck airborne.
It all comes down to buoyancy, of course. Helium is lighter than air and the difference in relative weights will give us the lift needed to launch the duck.
The University of Hawaii’s Chemistry Department provides some handy gas constants:
Standard Temperature and Pressure = 20 degrees C and 760 mm Mercury
STP = 760 mm pressure and 20 C
Weight of air per liter at STP = 1.20 gr/l
Weight of helium per liter at STP = 0.18 gr/l
Net lift per liter of helium at STP = 1.03 gr/l
The volume of a sphere is (4/3)πr3, so a perfectly spherical balloon with a 30cm diameter would have a volume of 14137.166941154 cubic cm, or 14.137 litres. That gives us a lift of 14.56 grams.
The next question is: How much does Daisy Duck weigh?
I’m going to assume that she is a normal size for a duck and, being completely white, probably a pekin which, Wikipedia reveals, grows to a weight of between 3.6 and 5 kilos. Taking the mid-point gives me a weight of 4.3 kilos for Daisy. Or 4300 grams.
That means we would need 296 helium balloons to launch Daisy Duck.