The flow rate of water from a tap of diameter `1.25cm` is `0.48` L/ min . The coefficient of viscosity of water is `10^(-3)` Pa s . After sometime the flow rate is increased to 3L/min. Characyerise the flow for both the flow rates .

Explanation

Diameter of cross section of tap d= 1.25cm
The volume of water flowing out per second (flux ) is ,
`Q=vA`
`Q=vxx(pid^(2))/(4) " " [becausevxxpir^(2)]`
`thereforev=(4Q)/(pid^(2))`
Raynold.s number `R_(e)=(rhovd)/(eta)=(4rhoQ)/(pietad)`
`=(4xx10^(3)xx0.48xx10^(3)xx10^(-6))/(3.14xx10^(-3)xx1.25xx10^(-2)xx60)`
`=0.0081528xx10^(5)`
`=815`
`therefore` For steady flow `R_(e)lt1000`
If `Q.=(3L)/(min)=(3xx10^(-3))/(60)=0.5xx10^(-4)(m^(3))/(s)`
`thereforeR_(e).=(4rhoQ.)/(pietad)`
`=(4xx10^(3)xx0.5xx10^(-4))/(3.14xx10^(-3)xx1.25xx10^(-2))`
`=0.5095xx10^(4)`
`R_(e)=5095`
Hence , `R_(e)gt3000` flow will be turbulent.