Pressure inside the zeppelin for it to float

[Fluid mechanics]

Homework Statement

A zeppelin of an ellipsoid shape (a=32m, b=c=a/3) iz filled with hydrogen. Pressure of the surrounding air is 100 000 Pa. Temperature of air and hydrogen is 20°C. The mass of an empty (not filled with hydrogen) zeppelin is 10 000 kg. What does the pressure of hydrogen inside the zeppelin have to be, so that the zeppelin floats in air?

Homework Equations

V=(4*π*a*b*c)/3
pV=nRT

The Attempt at a Solution

I got the volume of the zeppelin
V=(4*π*a*b*c)/3 = 2859,55 m³

Then I calculated the weight of this volume of air:

pV = mRT

m = (p*V)/(RT) = 3398,8 kg

And then i got stuck. Please help me.

 

[Orodruin]

What do you think m is and what are the units? Have you done the dimensional analysis of the ideal gas law including the units of all the involved quantities. Please post your full working with all of this.

 

[Andrew Mason]

Homework Statement

A zeppelin of an ellipsoid shape (a=32m, b=c=a/3) iz filled with hydrogen. Pressure of the surrounding air is 100 000 Pa. Temperature of air and hydrogen is 20°C. The mass of an empty (not filled with hydrogen) zeppelin is 10 000 kg. What does the pressure of hydrogen inside the zeppelin have to be, so that the zeppelin still floats in air?

Homework Equations

V=(4*π*a*b*c)/3
pV=nRT

The Attempt at a Solution

I got the volume of the zeppelin
V=(4*π*a*b*c)/3 = 2859,55 m³

Then I calculated the weight of this volume of air:

pV = mRT

m = (p*V)/(RT) = 3398,8 kg

And then i got stuck. Please help me.

Hi Fluid Mechanics. Welcome to PF!

I am not sure what the question is asking because if the Zeppelin was empty (no air, no hydrogen) it would still float. The addition of the hydrogen is to displace the air. To do that you just need to put in enough hydrogen to fill the volume at 100,000 Pa.

So maybe you have to just determine whether the Zeppelin floats with that much H. What is the condition required in order for the Zeppelin to experience positive buoyancy? What is the overall density of the Zeppelin with nothing inside? What is the mass of air that it displaces (assuming no air inside)? What is the mass of H at 100,000 Pa that fills that volume? Add that to the Zeppelin mass. Does the Zeppelin still float?

Check your calculation again for the volume of the ellipsoid. The formula is correct but your calculation is wrong. Just approximating: 4 x 32 x 10 x 10 = 12,800 m³

AM

 

[jbriggs444]

As I interpret the question, it is asking what partial pressure of Hydrogen is required so that the net buoyancy of the air-hydrogen mixture (at ambient pressure of one atmosphere, of course) is sufficient to support the craft.

Edit to add...

Of course in an actual Zeppelin using hydrogen for lift, one would not mix hydrogen with air in a rigid enclosure. Instead, one typically uses flexible hydrogen-filled gas bags within a rigid but vented enclosure. The hydrogen pressure within the bags is ambient, always. https://en.wikipedia.org/wiki/Airship

 

[Andrew Mason]

As I interpret the question, it is asking what partial pressure of Hydrogen is required so that the net buoyancy of the air-hydrogen mixture (at ambient pressure of one atmosphere, of course) is sufficient to support the craft.

That makes sense. But the question says it is "filled with hydrogen". It should say, "filled with a mixture of air and hydrogen" and ask what "partial pressure of hydrogen" would be required to make the ship float.

AM

 

[CWatters]

Its either a badly designed question or a trick question. Especially for anyone that knows how a Zeppelin worked (rather than some fictional rigid airship).

 

[Andrew Mason]

Its either a badly designed question or a trick question. Especially for anyone that knows how a Zeppelin worked (rather than some fictional rigid airship).

Yes. This Zeppellin with a mixture of air and hydrogen throughout would be a floating bomb. The Hindenburg at least tried to keep the hydrogen and air separate (but something obviously failed).

AM

 

[Tiran]

This certainly sounds like one of those questions is complicated and full of distractors, while the real answer is just "the same hydrogen pressure as the outside air pressure". But that's treating the zeppelin as a balloon, not a rigid structure full of balloons as they really are.

 

[Daily]

Yes. This Zeppellin with a mixture of air and hydrogen throughout would be a floating bomb. The Hindenburg at least tried to keep the hydrogen and air separate (but something obviously failed).

AM

As you may know, the Hindenburg had 63 flights before the accident. Flew as far as Rio de Janeiro. Graf Zeppelin made 590 flights totaling almost 1.7 million kilometers and first airship circumnavigate the world and first to flight non-stop across Pacific. 21 Zeppelins in total were made before WW1