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Problem 3.29

# Problem 3.29 - downward by l/2 The oil in the right leg is...

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Problem 3.29 [Difficulty: 2] Given: A U-tube manometer is connected to the open tank filled with water as shown (manometer fluid is Meriam blue) D 1 2.5 m = D 2 0.7 m = d 0.2 m = SG oil 1.75 = (From Table A.1, App. A) Find: The manometer deflection, l 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) Assumptions: (1) Static liquid (2) Incompressible liquid D 1 D 2 d c d Integrating the hydrostatic pressure equation we get: Δ p ρ g Δ h = When the tank is filled with water, the oil in the left leg of the manometer is displaced
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Unformatted text preview: downward by l/2. The oil in the right leg is displaced upward by the same distance, l/2. Beginning at the free surface of the tank, and accounting for the changes in pressure with elevation: p atm ρ water g ⋅ D 1 D 2 − d + l 2 + ⎛ ⎝ ⎞ ⎠ ⋅ + ρ oil g ⋅ l ⋅ − p atm = Upon simplification: ρ water g ⋅ D 1 D 2 − d + l 2 + ⎛ ⎝ ⎞ ⎠ ⋅ ρ oil g ⋅ l ⋅ = D 1 D 2 − d + l 2 + SG oil l ⋅ = l D 1 D 2 − d + SG oil 1 2 − = l 2.5 m ⋅ 0.7 m ⋅ − 0.2 m ⋅ + 1.75 1 2 − = l 1.600m =...
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