$9\mathrm{.}61$ Plot the local friction coefficient cf$,$ the boundary layer thick ness ratio $=$x$,$ and the drag coefficient Cf$,$ for both laminar and tur bulent boundary layers on a flat plate for Rx$,$ from $0$ to $500,000,$ assuming in the turbulent case that the layer is tripped at the leading edge and is fully turbulent along the length of the plate. Discuss the wave drag behavior? Is the boundary layer on the prototype predom inantly laminar or turbulent? Does the model boundary layer become turbulent at the comparable point? If not, the model boundary layer could be artificially triggered to turbulent by placing a tripwire across the hull. Where could this be placed? Estimate the skin$-$friction drag on model and prototype. $9\mathrm{.}64$Anuclear submarine cruises fully submerged at $27$ knots. The hull is approximately a circular cylinder with diameter D$=11$:$0$m and length L$=107$m$.$ Estimate the percentage of the hull length for which the boundary layer is laminar. Calculate the skin friction drag on the hull and the power consumed. $9\mathrm{.}65$ You are asked by your college crew to estimate the skin fric tion drag on their eight$-$seat racing shell. The hull of the shell may be approximated as half a circular cylinder with $457$ mm diameter and $7\mathrm{.}32$ m length. The speed of the shell through the water is $6$:$71$ m$=$s$.$ Estimate the location of transition from laminar to turbulent flow in the boundary layer on the hull of the shell. Calculate the thickness of the turbulent boundary layer at the rear of the hull. Determine the total skin friction drag on the hull under the given conditions. $9\mathrm{.}66$ The drag coefficient of a circular disk when placed normal to the flow is $1\mathrm{.}12.$ Calculate the force and power necessary to drive a $12$ in$.(0\mathrm{.}3$ m$)$ disk at $48$km$=$h through $($a$)$ standard air at sea level, and $($b$)$ water. $9\mathrm{.}67$Asteel sphere of $0\mathrm{.}25$ in$.$ diameter has a velocity of $200$ ft$=$sat an altitude of $30,000$ ft in the U$.$S$.$ Standard Atmosphere. Calculate the drag force on this sphere. $9\mathrm{.}68$Asteelsphere$$SG$=7$:$8$of$13$mmdiameterfallsataconstant velocity of $0$:$06$ m$=$s through an oil $$SG$=0$:$90.$ Calculate the vis cosity of the oil, assuming that the fall occurs in a large tank. $9\mathrm{.}69$ A sheet of plastic material $0\mathrm{.}5$ in$.$ thick, with specific gravity SG$=1$:$7,$ is dropped into a large tank containing water. The sheet is $2$ft$4$ft$.$ Estimate the terminal speed of the sheet as it falls with $($a$)$ the short side vertical and $($b$)$ the long side vertical. Assume that the drag is due only to skin friction, and that the boundary layers are turbulent from the leading edge. $9\mathrm{.}70$ In Section $7\mathrm{.}5$ the wave resistance and viscous resistance on a model and prototype ship were discussed. For the prototype, L$=130$m and A$=1800$m$2.$ From the data of Figs $7\mathrm{.}2$ and $7\mathrm{.}3,$ plot on one graph the wave, viscous, and total resistance $($N$)$ experienced by the prototype, as a function of speed. Plot a similar graph for the model. Discuss your results. Finally, plot the power $($kW$)$ required for the prototype ship to overcome the total resistance. ratio of drag forces as a function of Rx$.$