Question

The force, f, acting on the wings of an aircraft moving through air of velocity, v, and density, p, is given by the equation F=KVˣ Pʸ Aᶻ, and A is the surface area of the wings of the aircraft. Use dimensional analysis to determine the value of x, y and z

Answer 1

The values of x, y, and z in the equation F = K*V^x*P^y*A^z are x = 0, y = -1, and z = 0.

Step-by-step explanation:

The force, F, acting on the wings of an aircraft moving through air of velocity, v, and density, p, is given by the equation F = K*V^x*P^y*A^z, where A is the surface area of the wings of the aircraft. Using dimensional analysis, we can determine the values of x, y, and z.

First, let's look at the dimensions of each term in the equation:

• [F]: kg*m/s^2 (force)
• [K]: dimensionless constant
• [V]: m/s (velocity)
• [P]: kg/m^3 (density)
• [A]: m^2 (surface area)

Using the principle of dimensional homogeneity, we can equate the dimensions on both sides of the equation:

• [K]*[V]^x*[P]^y*[A]^z = kg*m/s^2
• dimensionless constant * (m/s)^x * (kg/m^3)^y * m^(2z) = kg*m/s^2

Equating the dimensions, we get the following system of equations:

• x: 1 = 0 (no m/s term)
• y: 0 = -1 (kg/m^3 term)
• 2z: 0 = 1 (m^2 term)

From these equations, we can conclude that x = 0, y = -1, and z = 0. Therefore, the values of x, y, and z in the equation F = K*V^x*P^y*A^z are x = 0, y = -1, and z = 0.