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• # Buoyancy Problems

Discussion in 'Calculations' started by aykhan90, Feb 16, 2014.

1. ### aykhan90New Member

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Feb 2014
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Hi

Recently I have been studying for the PE exam for Mechanical Engineers. I have been out of touch of studying for some time so I am having difficulty with some problems. These problems are not necessary difficult but I can't seem to understand how to go about solving them.

Problem 1)

A blimp contains 10000 lbm (4500 kg) of hydrogen (specific gas constant=766.5 ft-lbf/lbm-R (4124 J/kg.K) at 56 F (13 C) and 30.2 in HG (770 mm HG). What is its lift if the hydrogen and air are in thermal and pressure equilibrium?

I am not looking for the answer just some guidance on the method I should undertake to solve this.

Thanks

2.
3. ### VirguleActive Member

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Nov 2011
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Your blimp displaces the surrounding air. Every body experiences a certain lift since it displaces air and that air tries to regain its place. All body also have a weight dragging them down. Not all bodies though will experience a net lift. Only bodies displacing an amount of surrounding air heavier than their actual weight will experience that lift.

The force pulling down on the blimp (F1) is :

F1 = W = m x g = rho_blimp x g x V

where
W : total blimp weight in N
m : total blimp mass in kg
rho_blimp : density of the blimp's content (helium, ...) in kg/m3
g : gravitational constant in m/s2
V : volume displaced by blimp in m3

If you want to use F1 = rho_blimp x g x V, you're assuming the blimp's weight is equal to the gas content of it. In other words, that the mass of the frame, materials, ... are negligible.
You should use F1 = m x g for more accurate force.

Now the force (or lift) resulting from the displacement of the surrounding air, F2 is:

F2 = rho_air x g x V

where
rho_air : density of surrounding air in kg/m3
g : ...
V : ...

The net lift will be F2-F1.

Last edited: Feb 24, 2014

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