Problem $2$: $(50$ points$)$ You are designing a fountain that will be placed at the southern end of Lake Travis. The fountain is very simple in concept and is shown below. You have hired a geotechnical engineer to design the foundation. The geotechnical engineer wants to know the design forces she should use for the foundation. Specifically she wants the shear force and the overturning moment as shown in the figure. The flow rate through the fountain will be established by a pump $($mounted within the foundation$)$ and your target flow rate is $.$ You will use commercial steel pipe for the fountain and you may assume the manufacturer has specified that for the nozzle, Given the location you are concerned about the wind load on the fountain when the winds are out of the north and south. You have located an anemometer $($instrument to record wind speed$)$ at the proposed site for the past $3$ months and determined the design wind speed at an elevation of above the lake. For a wind out of the north $($i$.$e$.$ blowing to the south$)$ the design wind speed is and for a wind out of the south $($i$.$e$.$ blowing to the north$)$ the design wind speed is $.$ a$.$ What is the required output of the pump to generate the required flow rate? b$.$ What is the highest magnitude wind speed that occurs at the top of the fountain? You may assume a power law and$/$or the von Karman profile are reasonable boundary layer velocity profiles as appropriate. c$.$ What is the component of the drag force on the fountain due solely to wind for each of the north and south winds? You may neglect any forces due to water in the lake. d$.$ Which wind produces the worst$-$case total $?$ e$.$ Which wind produces the worst$-$case total $?$ f$.$ Solve for the worst case design total $.$ g$.$ Extra credit $-$ What is the typical shedding frequency of eddies from the fountain pipe under the design wind condition? State your assumptions.