The flow rate of water from a tap of diameter 1.25 cm is 0.481L/min. The coefficient of viscosity of water is 10^(-3)Pas (b) After sometimes 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 0.481L/min. T

1.	The flow rate of water from a tap of diameter 1.25 cm is 0.481L/min. The coefficient of viscosity of water is 10^(-3)Pas (b) After sometimes 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 thet tap be d=1.25 cm. 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//pi d eta` `=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)xx10^(-6)m^(3)s^(-1)`, we obtain `R_(e)=815` Since this is below 1000, the flowis 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