Question 5 (15 Points): Using "Dimensional Analysis" find the dimensionless equation, if prod =f(rho infty ,V_(infty ),c,mu _(infty )) and prod =rho _(infty )V_(infty )^hc^i doo' are given.

Question

Answer 1

To find the dimensionless equation using dimensional analysis, we need to equate the dimensions of the two given expressions for

.The dimensions of the given expressions are:

The dimensions of the variables are:

: density (M L^-3)

: velocity (L T^-1)

: specific heat capacity (M L^-2 T^-1)

: dynamic viscosity (M L^-1 T^-1)So, the dimensions of

are:

Now, let's consider the second expression for

:

The dimensions of this expression are:

To make the dimensions equal, we need to find the values of

and

such that:

Equating the powers of

and

, we get:

Solving for

and

, we get:

Therefore, the dimensionless equation is:

Hence, the dimensionless equation is:

Soru