Question

The thrust F of a screw propeller is known to depend upon the diameter d,speed of advance \nu ,fluid density p, revolution per second N, and the coefficient of viscosity μ of the fluid. Determine the dimensions of each of the variables in terms of L,M,T,and find an expression for F in terms of these quantities

Answer 1

Answer:

Dimension of diameter = L

Dimension of speed of advance, V = $LT^{-1}$

Dimension of N = $T^{-1}$

Dimension of coefficient of viscosity, μ = $ML^{-1} T^{-1}$

Dimension of Propeller thrust, $F = MLT^{-2}$

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 = $LT^{-1}$

The fluid density, p, is in kg/m³, hence the dimension = $ML^{-3}$

Rotation rate, N, is in Rev/s, hence the dimension = $T^{-1}$

coefficient of viscosity μ = $ML^{-1} T^{-1}$

The propeller thrust can be given by the formula:

$F = K_{T} \rho N^{2} d^{4}$

Where $K_{T}$ is the thrust coefficient

The dimension of the propeller thrust can then be derived as:

$F = ML^{-3} (T^{-1})^2 L^4\\F = ML^{-3}T^{-2}L^4\\F = MLT^{-2}$