Boundary Layer Theory:

A ship is $150$ m long and has a wetted area of $5000$m$^2.$ If it is encrusted with

barnacles, the ship requires $7000$ hp to overcome friction drag when moving in

seawater at U$=15$kn and $20$ degrees C $.($i$)$ What is the average roughness of

the barnacles? $($ii$)$ How fast would the ship move with the same power if the

surfaces were smooth?

Hint: For seawater, take rho$=1025$kg$//$m$^3$ and mu$=0\mathrm{.}00107$kg$//($ms$).$

Conversion: $1$kn$=0\mathrm{.}5144$m$//$s$.$ Recall Power$=$P$=$UD$.$

Do the work in the following order:

a$.$ Calculate the Reynolds number at the TE$,$ that is$,$ Re$\_$L$.$

b$.$ Decide if the flow should be treated as entirely turbulent or laminar.

c$.$ Calculate the drag force D $,$ then CD $.$

d$.$ Together from Fig. $7\mathrm{.}6$ and Equation $7\mathrm{.}48$ b calculate L$/$epsilon$,$ then

epsilon in meters.

e$.$ For the smooth case, calculate CD then D$.$

f$.$ Calculate U from D and the given P $.$