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Problem 3.34

# Problem 3.34 - pressure of the water p atm ρ Hg g ⋅ h 1...

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Problem 3.34 [Difficulty: 4] Given: Barometer with water on top of the mercury column, Temperature is known: h 2 6.5 in = h 1 28.35 in = SG Hg 13.55 = (From Table A.2, App. A) T7 0 ° F = p v 0.363 psi = (From Table A.7, App. A) Find: (a) Barometric pressure in psia (b) Effect of increase in ambient temperature on length of mercury column for the same barometric pressure: T f 85 °F = Solution: We will apply the hydrostatics equations to this system. Governing Equations: dp dh ρ g = (Hydrostatic Pressure - h is positive downwards) ρ SG ρ water = (Definition of Specific Gravity) h 2 Water vapor h 1 Water Mercury Assumptions: (1) Static liquid (2) Incompressible liquid Integrating the hydrostatic pressure equation we get: Δ p ρ g Δ h
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Unformatted text preview: pressure of the water: p atm ρ Hg g ⋅ h 1 ⋅ − ρ water g ⋅ h 2 ⋅ − p v = p atm p v ρ water g ⋅ SG Hg h 1 ⋅ h 2 + ( ) ⋅ + = p atm 0.363 lbf in 2 ⋅ 1.93 slug ft 3 ⋅ 32.2 × ft s 2 ⋅ lbf s 2 ⋅ slug ft ⋅ × 13.55 28.35 × in ⋅ 6.5 in ⋅ + ( ) × ft 12 in ⋅ ⎛ ⎝ ⎞ ⎠ 3 × + = p atm 14.41 lbf in 2 ⋅ = At the higher temperature, the vapor pressure of water increases to 0.60 psi. Therefore, if the atmospheric pressure were to remain constant, the length of the mercury column would have to decrease - the increased water vapor would push the mercury out of the tube!...
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