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

Options

A. 9:4
B. 3:2
C. `sqrt3 : sqrt2`
D. `sqrt2 : sqrt3`

Answer

A

Explanation

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" "[:. r_2=(d_2)/(2), r_1=(d_1)/(2)]`
`=(((3.75)/(2))/((2.5)/(2)))^2=(3.75/2.5)^2=9/4`