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Mechanical Properties Of Fluids

Question
CBSEENPH11020021
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(b) A large He balloon of volume 1425 m3 is used to lift a payload of 400 kg. Assume that the balloon maintains constant radius as it rises. How high does it rise?
[Take y0= 8000 m and ρHe = 0.18 kg m-3 ]

Solution
Density comma space straight rho space equals space Mass over Volume space space space space space space space space space space space space space space space space space space equals fraction numerator open parentheses Mass space of space the space payload space plus space Mass space of space helium close parentheses over denominator Volume end fraction space space space space space space space space space space space space space space space space space space space equals space fraction numerator open parentheses straight m space plus space Vρ subscript He close parentheses over denominator straight V end fraction space space space space space space space space space space space space space space space space space space equals space fraction numerator left parenthesis 400 plus 1425 cross times 0.18 right parenthesis over denominator 1425 end fraction space space space space space space space space space space space space space space space space space equals space 0.46 space kg divided by straight m cubed space And space in space the space previous space question space we space have space obtained comma space space space space space space space space space space space space space space space space space space space straight rho space equals space straight rho subscript straight o space straight e to the power of begin inline style bevelled fraction numerator negative space straight y over denominator straight y subscript straight o end fraction end style end exponent space space log subscript straight e open parentheses fraction numerator straight rho space over denominator space straight rho subscript straight o end fraction close parentheses space equals space minus straight y over straight y subscript straight o therefore space straight y space equals space minus 8000 cross times log subscript straight e space end subscript left parenthesis fraction numerator 0.46 over denominator 1.25 end fraction right parenthesis space space space space space space space space equals space minus 8000 space cross times space minus 1 space space space space space space space equals space 8000 space straight m space equals space 8 space km Therefore comma space the space balloon space will space rise space to space straight a space height space of space 8 space km. space

Some More Questions From Mechanical Properties of Fluids Chapter

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What is fluid?

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What is an ideal liquid?

Do liquids exert pressure?

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