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

The flow rate of water from a tap of diameter 1.25 cm is 0.48L/min. Th

1.	The flow rate of water from a tap of diameter 1.25 cm is 0.48L/min. The coefficient of viscosity of water is 10^(-3) Pa s. (b) After sometime the flow rate is increased to 3L/min. Characterise the flow for both the flow rates.
Answer» Solution :Let the speed of the flow be v and the diameter of the tap be `d=1.25cm`. The VOLUME of the water flowing out PER second is `Q=vxxpid^(2)//4""v=4Q//d^(2)pi` We then estimate the Reynolds number to be `R_(e)=4rhoQ//pideta` `=4XX10^(3)kgm^(-3)xxQ//(3.14xx1.25xx10^(-2)mxx10^(-3)Pas)` `=1.019xx10^(8)m^(-3)sQ` Since initially (a) `Q=0.48L//min=8cm^(3)//s` `=8xx10^(-6)m^(3)s^(-1)`, we obtain, `R_(e)=815` Since this is below 1000, the flow is steady. After some time (b) when `Q=3L//min=50cm^(3)//s` `=5XX10^(-5)m^(3)s^(-1)`, we obtain, `R_(e)=5095`. The flow will be turbulent.