Question

Water flows through a horizontal pipe of radius 'r' at a speed V. If the
radius of the pipe is doubled, the speed of flow of water under similar
1) 2 V
2) V/2
3) V/4
4) 4 V​

Answer 1

According to law of continuity
A1 * v1 = A2 * v2
—-> (r1)^2 * v1 = (r2)^2 * v2
Therefore the required answer is v/4

Answer 2

The speed of flow of water under similar conditions will be - 3) V/4

According to principle of continuity, "the rate at which mass enters a system is equal to the rate at which mass leaves the system plus the accumulation of mass within the system."

The formula is - A1V1 = A2V2

A = area

V = speed

R = radius

In the question, we have to find V2.

R1²V1 = R2²V2

R2 = 2R1

R1² V1 = (2R1)² V2

V2 = V1/4

Thus, new velocity will be 1/4 times of original velocity.