Question

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 ${10}^{-3}$ $Pa-s$. After sometime, the flow rate is increased to $3$ $L/min$. Characterize the flow for both the flow rates.

Answer 1

Let the speed of the flow be v and the area of tap be $d=1.2$ cm. The volume of the water flowing out per second is
$Q=v\times \pi d^2/4$
$v=4Q/d^2$
Reynold’s number is
$R_e=4P^{2}2/\pi d\eta$
$=4\times {10}^{3}kg/m^3\times Q/(3.14\times 1.2\times {10}^{-2}m\times {10}^{-1}Pas)$
$=1.061\times {10}^8{m}^{-3}s$ $Q=1.061\times {10}^{8}Q$
Initially,
$Q=0.48L/min=8.0c{m}^3/s$
$=8.00\times {10}^{-6}{m}^3/s$
we obtain
$R=484.8$
Since this is below 1000, the flow is steady.
After sometime when $Q=4L/min$,
$=66.67c{m}^3/s$
$=6.67\times {10}^{-5}{m}^3{s}^{-1}$
we obtain
$R=1.061\times {10}^8\times 6.67\times {10}^{-5}$
$=7076.9$
The flow now is turbulent.