Chapter 13, Problem 11RQ

The relationship of the power required by a propeller (show as the power number, on the ordinate) and the Reynolds number (abscissa) is shown in the following graph. For a propeller, the Reynolds number (Re) is written slightly differently as

$Re=\frac{D^{2}n\rho }{\mu }$

where D is the blade diameter [meters] and n is the shaft speed [hertz]. The power number (N_ρ) is given by the following, where P is the power required [watts].

$N_P=\frac{P}{\rho n^3{D}^5}$

Use the following chart to answer questions (a) through (d).

1. a. If the Reynolds number is 500, what is the power number for a system described by curve A?
2. b. If the power number (N_ρ) is 30, what is the Reynolds number for a system described by curve A?
3. c. If the Reynolds number is 4000, what is the power (P) required in units of watts at a shaft speed (n) of 0.03 hertz? Assume the system contains acetone, with a kinematic viscosity of 0.419 stokes. The density of acetone is 0.785 grams per cubic centimeters. Use curve B in the graph to determine your answer. (Hint: Use the Reynolds number of the system to first calculate the diameter, then find the power number, and then calculate the power.)
4. d. If the power number (N_ρ) is 5, what is the diameter (D) of the blade in units of centimeters at a shaft speed (n) of 0.02 hertz? Assume the system contains brine, with a kinematic viscosity of 0.0102 stokes. Use curve A in the graph to determine your answer. (Hint: Find the Reynolds number of the system first, and then calculate the diameter.)