Question 4 (extra credit*)

*This bonus question is used to award extra credit. Correctly answering this question is not

required to achieve full marks for the assignment.

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The figure above shows the cross-sectional elevation of a deployable flood barrier used to protect

a community from coastal flooding. The barrier has length I and mass per unit width m (i.e., total

mass per unit distance into the page) and is connected to a frictionless hinge at ground level. As

flood waters rise, the barrier rotates about the hinge and adopts a position with angle such that

hydrostatic equilibrium is achieved for a given inundation height h.

mg

a) Derive an expression for the water height h as a function of m, 1, and 0. You may assume that

the mass of the barrier is uniformly distributed. Assume a density of sea water p = 1025 kg/m³.

b) Assuming m = 500 kg/m and 1 = 6 m, plot the water height h as a function of 0 from 0 to 80°.

c) For the assumptions stated in (b), what is the maximum level of inundation that can be

accommodated by the barrier?