Ch 2. Fluid Statics Multimedia Engineering Fluids PressureVariation PressureMeasurement HydrostaticForce(Plane) HydrostaticForce(Curved) Buoyancy
 Chapter 1. Basics 2. Fluid Statics 3. Kinematics 4. Laws (Integral) 5. Laws (Diff.) 6. Modeling/Similitude 7. Inviscid 8. Viscous 9. External Flow 10. Open-Channel Appendix Basic Math Units Basic Equations Water/Air Tables Sections Search eBooks Dynamics Fluids Math Mechanics Statics Thermodynamics Author(s): Chean Chin Ngo Kurt Gramoll ©Kurt Gramoll

 FLUID MECHANICS - EXAMPLES Question 1 Telephone Pole Partially Submerged in a Lake   Problem Diagram A wooden telephone pole paritally falls into a lake as shown. What is the density of the pole? Assume the density of the water is 1.94 slug/ft3. Solution 1 The pole will come to a static position where the sum of the moments about the point O is equal to zero.      ΣMo = 0 Therefore, the buoyancy force multiplied by its lever arm must be equal and opposite the gravitational force times its lever arm.      ΣMo = 0 = (WpoleLpole - FBLB)cosθ where Lpole = L/2 (gravity acts uniformly along the entire length), and (buoyancy force acts at the centroid of the submerged part of the pole). Note, θ is not needed since it factors out of the equation. Summing moments at O gives,      WpoleLpole = FBLB where      Wpole = ρpole V g = ρpole (π r2 L) g      FB = ρwater V g = ρwater (π r2 L/3) g thus,       ρpole (π r2 L) g (L/2) = ρwater (π r2 L/3) g (5L/6) Cancelling terms,      ρpole (1/2) =(1.94 slug/ft3) (5/18) The density of the pole is      ρpole = 1.078 slug/ft3 Question 2 Septic Tank Septic tanks are used by homes in rural areas not serviced by sanitary sewers. Assume the tank is 6 ft x 6 ft x 10 ft (long) with 4 in. concrete walls, and assume 1 ft of soil over the tank. At what groundwater depth, d, if any, will the tank float? Any recommendations to keep it from floating? Assume γconcrete = 150 pcf, γsoil = 120 pcf, and γwater = 62.4 pcf Solution 2 Inside dimensions: h, w, l Outside dimensions: h + 2t, w + 2t, l + 2t where t is the wall thickness      Vc = (h + 2t)(w + 2t)(l + 2t) - hwl      A = (w + 2t)(l + 2t) Since there is 1 ft of soil over the top of tank,      z = (1 ft) + (h +2t) - d where d is the water table.      γconcrete = 150 pcf      γsoil = 120 pcf      γwater = 62.4 pcf To float, the buoyancy force acting on the bottom of the tank must be greater than the weight of the tank and the soil on top.       septic tank: h = 6 ft, w = 6 ft, l = 10 ft, t = 4 in.      Vc = 474.1 - 360 = 114.1 ft3      A = 71.11 ft2      z = 7.67 - d       If the groundwater table depth is less than 1.89 ft, the septic tank will float. Recommendation to keep it from floating: use 6 in. walls instead of 4 in.

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