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    Size of a hydrogen spherical balloon for lifting a payload

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    Determine the size of a spherical balloon filled with hydrogen at 30°C and atmospheric pressure for lifting 400Kg payload. Atmospheric air is at temperature of 27°C and barometer reading is 75 cm of mercury.

    © BrainMass Inc. brainmass.com September 29, 2022, 9:49 pm ad1c9bdddf
    https://brainmass.com/engineering/mechanical-engineering/size-hydrogen-spherical-balloon-lifting-payload-537508

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    Qn. Determine the size of a spherical balloon filled with hydrogen at 30°C and atmospheric pressure for lifting 400Kg payload. Atmospheric air is at temperature of 27°C and barometer reading is 75 cm of mercury.

    Given :
    Hydrogen temperature = 30°C = 303K
    Load lifting = 400Kg
    Atmospheric pressure = 1.00 bar
    Atmospheric Temperature = 27°C = 300K

    Solution:

    Mass of air displaced by balloon(ma) = Mass of balloon hydrogen gas (mb) + load lifted........(i)
    Since PV = mRT;
    ma= PaVa /RTa;
    where R = 8314/29 = 287 KJ/KgK (Mol. wt of air=29)

    ma = (1 x 105 x V)/ 287 x 300
    = 1.162Vkg................................................(ii)

    Mass of balloon with hydrogen, mb = PV/RT
    = (1 x 105 x V)/ {(8314/2) x 300}
    = 0.08Vkg.......................(iii)
    Putting the values of (ii) and (iii) in equation (i)
    1.168V = 0.08V + 400
    V = 369.67m3.
    But we know that the volume of a balloon (sphere) V= 4/3Πr3
    Substituting for V we get, r = 4.45m. (ANS)

    This content was COPIED from BrainMass.com - View the original, and get the already-completed solution here!

    © BrainMass Inc. brainmass.com September 29, 2022, 9:49 pm ad1c9bdddf>
    https://brainmass.com/engineering/mechanical-engineering/size-hydrogen-spherical-balloon-lifting-payload-537508

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