A single pipe of diameter x has to be replaced by six pipes of diameters 12 cm each. The pipes are used to covey some liquid in a laboratory. If the speed/flow of the liquid is maintained the same then the value of x is ?

Volume of water flowing through 1 pipe of diameter x = Volume discharged by 6 pipes of diameter 12 cms.

As speed is same, area of cross sections should be same. 

Area of bigger pipe of diameter x = Total area of 6 smaller pipes of diameter 12 

i.e  $\mathrm{\pi R}2 = 6\mathrm{\pi R}12$   

Here R = R and R1 = 12/2 = 6   

$\Rightarrow R2 = 6\times 6\times 6$   

R = 14.696   

=> D = X = 14.696 * 2 = 29.3938 cm.