Question

The mean of the summation of two flow variables will be equal to ____________

(a) the summation of their mean components – the summation of the mean of their fluctuating components

(b) the summation of their mean components + the summation of the mean of their fluctuating components

(c) the summation of their fluctuating components

(d) the summation of their mean components

This question was posed to me in quiz.

Enquiry is from Turbulence Modelling in portion Turbulence Modelling of Computational Fluid Dynamics

Answer 1

Correct option is (d) the summation of their mean components

The best explanation: Consider two flow variables which can be decomposed as a=A+a’ and b=B+b’. The mean of their summation means

a+b = A+a’+B+b’

But, a’ = 0 and b’ = 0. Therefore,

a+b = A+B

Also, A = A and B = B. Hence,

a+b = A+B.