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 conditions is

Answer 1

If the radius of the pipe is doubled ,the speed of water under similar condition is decreased by 4 times of initial speed.

• Flow rate (Q) can be expressed in terms of velocity(V) and area(A).

• It is the volume of fluid that pass through a surface in unit time.

                                        Q=V×A

• Equation of continuity can be explained using Flow rate.

• Equation of continuity says when Area increases Speed decreases and vice versa.That is,

                                AV=a constant

• Here radius 'r'get doubled to ' 2r ' .

• Since area is directly proportional to the square of radius(r²),area increases to  4 times.

• That is if initial area is A1 after doubling radius the new area will be 4 times of A1.

• Since area increases 4 times the velocity of fluid decreases by 4 times of initial velocity.