Question

An incompressible non viscous fluid flows

steadily through a cylindrical pipe which has

radius 2R at point A and radius R at point B

farther along the flow direction. If the velocity

of the fluid at point A is V, its velocity at the

point B will be

(a) V/2 (b) 4V

(c) 2V (d) V​

Answer 1

Using the Equation of the continuity which says that the area of the cross section of cylindrical pipe is inversely proportional to the velocity.

Thus, In Terms of the mathematics, It can be expressed as,

 A₁V₁ = A₂V₂ ,

where A₁ is the area of cross-section at Point A, and V₁ is the velocity of the fluid at A. Also, A₂ is the area of cross-section at Point B, and V₂ is the velocity of the fluid at B.

A₁ = π(2R)² = 4πR², V₁ = V, A₂ = π(R)² = πR² and V₂ = ?

Now,  4πR² × V = πR² × V₂

V₂ = 4V

Hence, Option (b). is correct.

Hope it helps.