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

Dimension of diameter = L

Dimension of speed of advance, V =

Dimension of N =

Dimension of coefficient of viscosity, μ =

Dimension of Propeller thrust,

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 =

The fluid density, p, is in kg/m³, hence the dimension =

Rotation rate, N, is in Rev/s, hence the dimension =

coefficient of viscosity μ =

The propeller thrust can be given by the formula:

Where is the thrust coefficient

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

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explanation: