This question involves the concepts of drag coefficient, drag force, characteristic length, and Reynolds number.
(a) The drag force is found to be "498.6 N".
(b) Reynolds number is found to be "3.744 x 10⁶".
(a)
The drag force on the dolphin can be found using the following formula:
[tex]F = \frac{1}{2}\rho CAv^2[/tex]
where,
F = drag force = ?
[tex]\rho[/tex] = density = 1000 kg/m³
C = drag coefficient = 0.09
A = Area = [tex]\frac{\pi d^2}{4}=\frac{\pi (0.5\ m)^2}{4} = 0.197\ m^2[/tex]
v = speed = 7.5 m/s
Therefore,
[tex]F = \frac{1}{2}(1000\ kg/m^3)(0.09)(0.197\ m^2)(7.5\ m/s)^2\\\\[/tex]
F = 498.6 N
(b)
The Reynolds number can be found using the following formula:
[tex]Re = \frac{\rho vd}{\mu}[/tex]
where,
Re = Reynolds number = ?
[tex]\rho[/tex] = density = 1000 kg/m³
d = characteristic length = 0.5 m
μ = dynamic viscosity of water at 20° C = 1.0016 x 10⁻³ Pa.s
Therefore,
[tex]Re = \frac{(1000\ kg/m^3)(7.5\ m/s)(0.5\ m)}{1.0016\ x\ 10^{-3}\ Pa.s}[/tex]
Re = 3.744 x 10⁶
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