GATE 2023 CH – Question 33
The viscosity of an incompressible Newtonian fluid is measured using a capillary tube of diameter 0.5 mm and length 1.5 m. The fluid flow is laminar, steady and fully developed. For a flow rate of 1 cm$^3$s$^{-1}$, the pressure drop across the length of the tube is 1 MPa. If the viscosity of the fluid is $k \times 10^{-3}$ Pa s, the value of $k$ is ___________ (rounded off to two decimal places).
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Show answer and explanation
Correct answer: 1.01 to 1.03
Explanation
The Hagen-Poiseuille equation gives $\Delta P = \frac{128\mu LQ}{\pi D^4}$. So $\mu = \frac{\pi D^4\Delta P}{128LQ} = \frac{\pi \times (0.5 \times 10^{-3})^4 \times 10^6}{128 \times 1.5 \times 10^{-6}} = 1.0227 \times 10^{-3}$ Pa s, so $k = 1.02$.