Final answer:
The Reynolds number is dimensionless, and this is shown by substituting the units for each quantity in its definition (fluid density, velocity, radius, and viscosity) and demonstrating that all the units cancel out, leaving a unitless value.
the correct answer is d) [NR] = 1.
Step-by-step explanation:
The Reynolds number (NR) is a dimensionless number used to predict the flow regime in a pipe system, either laminar or turbulent.
It is defined by the equation NR = (p * v * r) / n, where p stands for the fluid density (measured in kg/m^3), v for the fluid velocity (measured in m/s), r for the tube radius (measured in m), and n for the viscosity of the fluid (measured in kg/(m*s)).
To show that the Reynolds number is unitless, we can substitute these units into the equation and cancel out the terms, as follows:
NR = (kg/m^3 * m/s * m) / (kg/(m*s))
NR = (kg * m * m) / (s * m^3) * (m * s / kg)
NR = (kg * m^2) / (s * m^3) * (m * s / kg)
NR = 1
All units cancel out, leaving the Reynolds number as a dimensionless quantity, which establishes that the correct answer is d) [NR] = 1.