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. `sqrt(3) : sqrt(2)`
D. `sqrt(2) : sqrt(3)`

Answer

A

Explanation

As given
`d_(1)=`Diameter of Ist pipe is 3.75.
`d_(2)=`Dimeter of IInd pipe is 3.75.
Applying equation of continuty for cross-sections `A_(1)" and "A_(2)`.
`rArr" "A_(1)v_(1)=A_(2)v_(2)rArrv_(1)/v_(1)=A_(2)/A_(2)=(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)):}]`