Question

An ideal fluid flows through a pipe of circular cross-section made of two sections with diameters `2.5 cm` and `3.75 cm`. The ratio of the velocities in the two pipes is
A. `9:4`
B. `3:2`
C. `sqrt(3):sqrt(2)`
D. `sqrt(2):sqrt(3)`

Answer 1

Correct Answer - A
Consider the diagram where an ideal fluid is flowing through a pipe.

As given
`d_(1)`=Diameter at 1st point is 2.5.
`d_(2)` =Diameter at 2nd point is 3.75.
Applying equation of continuity for cross-sections `A_(1)` and `A_(2)`.
`implies A_(1)v_(1)=A_(2)v_(2)`
`implies (v_(1))/(v_(2))=(A_(2))/(A_(1))=(pi(r_(2)^(2)))/(pi(r_(1)^(2)))=((r_(2))/(r_(1)))^(2)`
`=(((3.75)/(2))/((2.5)/(2)))^(2)=((3.75)/(2.5))^(2)=(9)/(4){:[(r_(2)=(d_(2))/(2)),(r_(1)=(d_(1))/(2))]:}`