hw_3 - gate surface is x = y 2 /a D = 4m air at P atm air...

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HW #3: MMAE 310 Spring 2007 1. Consider the example discussed at the end of class on Thursday, February 01, 2007. The equation of the curved gate surface is x = y 2 /a, with a = 4 m. The gate width (into the page) is 5m. a) Find the magnitudes of the resultant horizontal and vertical forces and b) find the location where the resultant horizontal force acts and find the location where the resultant vertical force acts . 2. Find the magnitude and location of the resultant force on the hemispherical dome shown in the figure 3. For the gate shown, α = 45 ° , y 1 = 1m and y 2 = 3 m. Will the gate fall or stay in position under the action of the hydrostatic and gravity forces if the gate itself weights 90 kN and is 1.0 m wide? Assume T = 10 ° C. g r x g r air at P atm y water air at P atm Equation of
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Unformatted text preview: gate surface is x = y 2 /a D = 4m air at P atm air at P atm y 1 water air at P atm y 2 gate hinge water water + h = 9' Hemisphere R = 4' air at P atm g r 4. Determine the resultant hydrostatic force F on the triangular gate, which is hinged at the bottom edge and held by the reaction R T at the upper corner. Express F in terms of , h and W. Also determine the ratio R T /F. Neglect the weight of the gate. 5. Determine the minimum volume of concrete ( concrete = 23.6 kN/m 3 ) needed to keep the gate (1-m wide) in a closed position, l = 2m. Note the hinge at the bottom of the gate. air at P atm air at P atm hinge l W hinge View A-A water A A h h F water R T l Submerged concrete block hinge water stop gate g r g r air at P atm...
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hw_3 - gate surface is x = y 2 /a D = 4m air at P atm air...

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