CVE_240-Assignement_3_CHAPTER_3__Solutions - American...

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Unformatted text preview: American University of Sharjah Civil Engineering Department CVE 240 – FLUID MECHANICS Assignment 3_SOLUTIONS is Q.1) Gate AB in Figure 1 is 2m wide in to the paper, hinged at A, and restrained by a stop at B. The water is at 10 oC. If the water depth h=3.5 m, compute If a) The force on stop B b) The reactions at A (with zero gate weight). (Answers 44.24kN, 36.7kN, 0) Solution: The centroid of AB is 0.75m below A, hence the centroidal depth is h -1.5+0.75 = 2.75 ft. Then The the total hydrostatic force on the gate is the F=γ hCG Agate=(9.810 )(2.75)(1.5*2) = 80.93kN (9.810 The C.P. is below the centroid by the amount _ _ y cp = y + I _ yA = 2.75 + 2 * 1.5 3 / 12 = 2.82m 2.75 * (2 * 1.5) This is shown on the freebody of the gate. We find force Bx with moments about A: ΣMA=0 F*0.82-Bx*1.5=0⇒Bx=44.24kN The reaction force at A then follow from equilibrium of forces (with zero weight) ΣFx=0 80.93-44.24-Ax=0⇒Ax=36.7kN 80.93 ΣFx=0 Az=0 =0 Q.2) Determine the resultant forces due to the water acting on the submerged rectangular panels A and B shown in Figure 2. Panel A has an area of 2m x 1m, and panel B an area of 2m x 1.5m. At what points do these forces act? (Answers 49050 N-2.63m & 50240 N-2.55m) 2.63m Solution: _ _ I 1 * 2 3 / 12 y cp = y + _ = 2.5 + = 2.63m F=γ hCG Agate=9810*(1.5+1)(2*1)=49050 N 2 .5 * ( 2 .5 * 2 ) yA _ _ F=γ hCG Agate=9810*(1+1*Sin45)*(2*1.5)=50240 N 1+1*Sin45 y cp = y + I _ yA = 2.41 + 1.5 * 2 3 / 12 = 2.55m 2.41 * (1.5 * 2) Q.3) The rectangular gate CD is 2 m wide and 2.5 m long (Figure 3). Neglecting the friction at the hinge C, determine the weight of the gate necessary to keep it shut until the water level rises to 2m above the hinge. (Answer PB=272.7kN) Q.4) A 2-m wide gate OAB is hinged at O and rest against a rigid support at B as shown in Figure 4. What minimum horizontal force, P, is required to hold the gate closed? Neglect the weight of the gate. (Answer 241.7N) Solution: Q.5) A bulkhead 5 m long divides a storage tank. One side of the tank is filled with oil of density 800 kg/m3 to depth of 2 m and the other side is filled with water to a depth of 1 m, as shown in Figure 5. Determine the resultant pressure force and its location. Solution: ...
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This note was uploaded on 01/24/2012 for the course ECON 101 taught by Professor Dezhbakhsh during the Spring '07 term at Emory.

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