The rate of flow varies inversely as the square of the radius of the pipes.
This relationship is expressed as:
Rate ∝r21
For two pipes:
Rate2Rate1=r12r22
The diameter of pipe 1 is 2 cm, so:
r1=22=1 cm
The diameter of pipe 2 is 4 cm, so:
r2=24=2 cm
Applying the inverse square relationship:
Rate2Rate1=r12r22
Rate2Rate1=(1)2(2)2
Rate2Rate1=14
Therefore, the ratio of the rates of flow is 4:1.