Answer:
Dimension of diameter = L
Dimension of speed of advance, V = [tex]LT^{-1}[/tex]
Dimension of N = [tex]T^{-1}[/tex]
Dimension of coefficient of viscosity, μ = [tex]ML^{-1} T^{-1}[/tex]
Dimension of Propeller thrust, [tex]F = MLT^{-2}[/tex]
Explanation:
The unit of diameter, d is meters, hence dimension of d = L
The speed of advance, V is in m/s, hence the dimension = [tex]LT^{-1}[/tex]
The fluid density, p, is in kg/m³, hence the dimension = [tex]ML^{-3}[/tex]
Rotation rate, N, is in Rev/s, hence the dimension = [tex]T^{-1}[/tex]
coefficient of viscosity μ = [tex]ML^{-1} T^{-1}[/tex]
The propeller thrust can be given by the formula:
[tex]F = K_{T} \rho N^{2} d^{4}[/tex]
Where [tex]K_{T}[/tex] is the thrust coefficient
The dimension of the propeller thrust can then be derived as:
[tex]F = ML^{-3} (T^{-1})^2 L^4\\F = ML^{-3}T^{-2}L^4\\F = MLT^{-2}[/tex]
