The mass of the liquid flowing per second per unit area of cross-section of the tube is proportional to (pressure difference across the ends)^(n) and (average velocity of the liquid)^(m) . Which of the following relations between m and n is correct?

Options

A. `m=n`
B. `m=-n`
C. `m^(2)=n`
D. `m=-n^(2)`

Answer

B

Explanation

According to the question,
we have, `(m)/(t.A)propp^(n).v^(m)orm//t.A=kp^(n)v^(m)`
where, `k` is proportionality constant.
Using principle of homogeneity, we get
`" "["ML"^(-2)"T"^(-1)]=k["ML"^(-1)"T"^(-2)]^(n).["LT"^(-1)]^(m)`
or `" "["ML"^(-2)"T"^(-1)]=k["M"]^(n)["L"]^(-n+m)["T"]^(-2n)`
Equating both sides, we find `n=-m or m=-n`