Water is flowing throug a tube of radius r with velocity v. If the tube is connected to another tube of radius `(r)/(2)`. Then select a correct statement from the follwing statements.

Options

A. Velocity of water in the second tube is v.
B. Velocity of water in the second tube is 2v.
C. Velocity of water in the second tube is `(v)/(2)`.
D. Velocity of water in the second tube is 4v.

Answer

D

Explanation

From the equation of continuity of flow we get
`a_(1)v_(1)=a_(2)v_(2)`
`pir_(1)^(2)v_(1)=pir_(2)^(2)v_(2)`
`(v_2)/(v_1)=(r_(1)^(2))/(r_(2)^(2))=(r^2)/((r/2)^(2))=4`
`thereforev_(2)=4v_(1)`