Answer to Question #142584 in Electric Circuits for wqae

Question

The power, P, obtainable from a wind turbine may be given by P = KL^2p*V^3
Where L = length of the blades, p*= 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 common degree.

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

c) 1) it is also impossible to determine dimensionless quantities using this method.

2) the dimension method may assume an error in the physical direction of the solution, but it cannot assume an error in mathematical action.