Answer to Question #198223 in Mechanical Engineering for lihle

Question #198223

the face of a dam is vertical to a depth of 5 m below the water surface and then slopes at 30 degrees to the vertical. If the depth of the water is 9 m,completely specify the resultant force per metre run acting on the whole face. Use equilibrium of vector to find the final answer


1
Expert's answer
2021-05-31T06:08:41-0400

Depth"=5m"

"\\theta=30^0"

Depth"=9m"

Projected area ,"A_p=h*w=9*1=9m^2"

"h=\\frac{9}{2}=4.5m"

Volume above the inclined plate, "V=[Xh_2+\\frac{h_1x}{2}]w"

V"=(\\frac{7.5}{tan60}*5+\\frac{1}{2}*7.5*\\frac{7.5}{tan60})=37.9m^3"

Horizontal component of force on the dam

"F_x=r_wAP\\bar{h}=9810*9*4.5=397305"

Vertical component

"F_y=r_w*v=9810*37.9=159316.2N"

Resultant, R"=\\sqrt{F_x^2+F_y^2}{}=\\sqrt{397305^2+159316^2}"

"=1641955.06N"

"tan\\theta=\\frac{F_y}{F_x}=\\frac{159316.2}{397305}=0.4"

"\\theta=tan^{-1}0.4=21.8" from positive axis in clockwise direction



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