GATE 2023 CE (CE1) – Question 63
A flocculator tank has a volume of 2800 m$^3$. The temperature of water in the tank is 15°C, and the average velocity gradient maintained in the tank is 100/s. The temperature of water is reduced to 5°C, but all other operating conditions including the power input are maintained as the same. The decrease in the average velocity gradient (in %) due to the reduction in water temperature is _____ (round off to nearest integer).
[Consider dynamic viscosity of water at 15°C and 5°C as $1.139 \times 10^{-3}$ N-s/m$^2$ and $1.518 \times 10^{-3}$ N-s/m$^2$, respectively]
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Correct answer: 13
Explanation
The velocity gradient is $G = \sqrt{\frac{P}{\mu V}}$. With the power and the volume fixed, $G \propto \mu^{-1/2}$. So $\frac{G_5}{G_{15}} = \sqrt{\frac{1.139}{1.518}} = 0.866$, and the decrease is $(1 - 0.866) \times 100 = 13.4\%$, about 13%.