Question

The thrust F of a screw propeller is known to depend upon the diameter d,speed of advance \\u ,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

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)`

Step-by-step 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)`