What is the maximum flow rate of water (in `m^(3) s^(-1)`) for laminar flow in a pipe having diameter of `6` cm. Given that coefficent of viscosity of water is `0.01` poise. Density of water `10^(3) kg m^(-3)`.

Explanation

Here, diameter `D=6 cm =0.06 m`,
`rho =10^(3) kg m^(-3), eta=0.01 poise =(0.01)/(10)` deca poise
`=10^(-3)` deca poise
Critical velocity of the flow of liquid is given by
`v_(c)=(Neta)/(rhoD)`
For laminar flow, the maximum value of `N=2000`
`:. v_(max)=(2000xx10^(-3))/(10^(3)xx0.06)`
Flow rate of water for laminar flow
`V=piD^(2)0/(4)xxv_(max)=(3.142xx(0.06)^(2))/(4)xx(2000xx10^9-3)/(10^(3)xx0.06)`
`=9.4xx10^9-5 m^(3) s^(-1)`