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

1.	The flow rate of water from a tap of diameter 1.25 cm is 0.48 L/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 = 1.25 CM. The VOLUME of the water flowing out per second is `Q = v xx pi d^2//4 ""v= 4Q//d^2pi ` We then estimate the REYNOLDS number to be `R_e = 4pQ//pi d eta` `= 4 xx 10^3 kg m^(-3) xx Q(3.14 xx 1.25 xx 10^(-2) m xx 10^(-3) Pa s)` `= 1.019 xx 10^(8) m^(-3) sQ` SINCE INITIALLY (a) Q = 0.48 L/min = `8 cm^3//s` `= 8 xx 10^(-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 = 50 `cm^3//s` `= 5xx 10^(-5) m^3 s^(-1)` we obtain , `R_e = 5095`. The flow will be turbulent.