Question 10.19: Figure 10.21 illustrates variation of the wave drag coeffici...

(a)–(b) The planform area is used to compute the drag force for the hull, and the drag force is determined by applying Equation 10.12 F_{D} = C_{D} \frac{1}{2} \rho v^{2}A . The fluid properties for the ocean water (saltwater) is given in Table A.4 in Appendix A.
(a) The drag force on a hull without a bow bulb/streamlined body is determined as follows:

slug: = 1 lb \frac{sec^{2}}{ft}                           L: = 50 ft                           A_{plan}: = L^{2} =2.5 \times 10^{3} ft^{2}

V: = 7.5 mph = 11 \frac{ft}{s}                           g: = 32 . 174 \frac{ft}{sec^{2}}                           F: = \frac{V}{\sqrt{g.L} } = 0.274                           \rho : = 1985 \frac{slug}{ft^{3}}

Guess value:                          F_{D}: = 1 lb

Given

F_{D} = C_{D} \frac{1}{2} \rho.V^{2} . A_{plan}
F_{D}: = Find (F_{D}) = 225.173 lb

(b) The drag force on a hull with a bow bulb/less streamlined body is determined as follows:

Guess value:                          F_{D}: = 1 lb

Given

F_{D} = C_{D} \frac{1}{2} \rho.V^{2} . A_{plan}
F_{D}: = Find (F_{D}) = 75.058 lb

Therefore, because for a given velocity (and thus, a given F) the drag coefficient, C_{D} for the hull without a bow bulb/streamlined body is 3 times that for the hull with a bow bulb/less streamlined body; the corresponding drag force for the hull without a bow bulb/streamlined body is also 3 times that for the hull with a bow bulb/less streamlined body, as the drag force, F_{D} is directly proportional to the drag coefficient, C_{D} (see Equation 10.12 F_{D} = C_{D} \frac{1}{2} \rho v^{2}A ).