An ideal fluid flows (laminar flow) through a pipe of non-uniform diameter. The maximum and minimum diameters of the pipes are 6.4cm and 4.8cm, respectively. The ratio of minimum and maximum velocities of fluid in this pipe is

Options

A. `(81)/(256)`
B. `(9)/(16)`
C. `(3)/(4)`
D. `(3)/(16)`

Answer

B

Explanation

From continuity equation, `A_(1) v_(1) = A_(2) v_(2)`
`:. (v_(1))/(v_(2)) = (A_(2))/(A_(1)) " " (A_(2))/(A_(1)) = ((pi D_(2)^(2))/(4))/((pi D_(1)^(2))/(4)) = (D_(2)^(2))/(D_(1)^(2))`
`:. (v_(1))/(v_(2)) = ((D_(2))/(D_(1)))^(2)`
`:. (v_(1))/(v_(2)) = ((4-8)/(6-4))^(2) = ((3)/(4))^(2)`
`:. (v_(1))/(v_(2)) = (9)/(16)`