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: sqrt 3`

Answer

A

Explanation

As given
`d_1` = Diameter of Ist pipe is 2.5
`d_2`= Diameter of Iind pipe is 3.75
Applying equation of continuity for cross sections `A_1 " and " A_2`
`rArr A_1v_1 = A_2v_2 rArr 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)]`