Answer to Question #142583 in Electric Circuits for Nama Glory

Question

The power, P, obtainable from a wind turbine may be given by P = KL2PV3
Where L = length of the blades, pg Air density, and v = wind speed.
The equation is homogenous.
(a) What is a homogenous equation?
(b) Determine the base units of the constant K.
(c) State two shortcomings of using homogeneity to check the correctness Of a physical equation.

Answer 1

a) Homogeneous equations are equations in which all terms have the same total degree.

b)$K=\frac{P}{L^2\times p_g\times v^3}$ , therefore $[K]=\frac{\frac{kg\times \frac{m}{s^2}\times m}{s}}{m^2\times \frac{kg}{m^3}\times \frac{m^3}{s^3}}=1$ , $K$ is a dimensionless quantity.

c) 1) the dimension Method can suggest the error of the physical direction of the solution, but it cannot suggest the error of the mathematical action.

2) It is also impossible to determine dimensionless values using this method.