Answer to Question #107512 in Mechanical Engineering for abbas

Question

The pressure difference p of air that flows through a fan is a function of the diameter D of the blade, its angular rotation, density of the air, and the flow Q. Use the FLT method of repeating variables to generate a dimensionless relationship between these parameters

Answer 1

In FLT method of dimension we take F(Force), L(Length) and T (Time ) as standard dimension and find the dimension of other quantities in terms of FLT

Here pressure difference is function of diameter of blade(D), Angular rotation(), density of air ( ) and the flow (Q).

Now here equate the dimension of the above quantities in terms of FLT

now equate the dimension of all the quantities in above equation

On comparing with the dimensions of the above quantities we can say that

on comparing the power of dimension we can say that,

c=1,

2 c-d=0

2 c=d

d=2,

a-4c+3d=-2

1-4+6=-2

a=-5

so from here we can say that the relation is as follows

k