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Problem 3.91

# Problem 3.91 - net F air ρ w g ⋅ V d ⋅ − = and V d F...

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Problem *3.91 [Difficulty: 2] Given: Specific gravity of a person is to be determined from measurements of weight in air and the met weight when totally immersed in water. Find: Expression for the specific gravity of a person from the measurements. Solution: We will apply the hydrostatics equations to this system. Governing Equation: F buoy ρ g V d = (Buoyant force is equal to weight of displaced fluid) F net F buoy Mg Assumptions: (1) Static fluid (2) Incompressible fluid Taking a free body diagram of the body: Σ F y 0 = F net M g F buoy + 0 = F net is the weight measurement for the immersed body. F net M g F buoy = M g ρ w g V d = However in air: F air M g = Therefore the weight measured in water is: F
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Unformatted text preview: net F air ρ w g ⋅ V d ⋅ − = and V d F air F net − ρ w g ⋅ = Now in order to find the specific gravity of the person, we need his/her density: F air M g ⋅ = ρ g ⋅ V d ⋅ = ρ g ⋅ F air F net − ( ) ρ w g ⋅ ⋅ = Simplifying this expression we get: F air ρ ρ w F air F net − ( ) = Now if we call the density of water at 4 deg C ρ w4C then: F air ρ ρ w4C ⎛ ⎜ ⎝ ⎞ ⎟ ⎠ ρ w ρ w4C ⎛ ⎜ ⎝ ⎞ ⎟ ⎠ F air F net − ( ) = SG SG w F air F net − ( ) ⋅ = Solving this expression for the specific gravity of the person SG, we get: SG SG w F air F air F net − ⋅ =...
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