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Problem 3.35

# Problem 3.35 - Problem 3.35 Given[Difficulty 3 U-tube...

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Problem 3.35 [Difficulty: 3] Given: U-tube manometer with tubes of different diameter and two liquids, as shown. d 1 10 mm = d 2 15 mm = SG oil 0.85 = Find: (a) the deflection, h, corresponding to (b) the sensitivity of the manometer Δ p 250 N m 2 = Solution: We will apply the hydrostatics equations to this system. Governing Equations: dp dz ρ g = (Hydrostatic Pressure - z is positive upwards) ρ SG ρ water = (Definition of Specific Gravity) h AB l 1 p atm l 2 l w l 3 l 4 p atm p atm + Δ p p atm Assumptions: (1) Static liquid (2) Incompressible liquid Integrating the hydrostatic pressure equation we get: pp o ρ g zz o () = ρ g z o z = From the left diagram: p A p atm ρ water g l 1 = ρ oil g l 2 = 1 From the right diagram: p B p atm Δ p + ρ water g l 3 = 2 p B p atm ρ water g l 4 ρ oil g l 2 + = 3 Combining these three equations: Δ p ρ water g l 4 l 3 ρ oil g l 2 + = ρ water g l 4 l 1 + l 3 =

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Problem 3.35 - Problem 3.35 Given[Difficulty 3 U-tube...

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