Question

A liquid flows through a pipe of $1.0mm$ radius and $10cm$ length under a pressure of ${10}^{4}dynec{m}^{-2}$. Calculate the rate of flow and the speed of the liquid coming out of the tube. The coefficient of viscosity of the liquid is $1.23$ centipoises.

• A. $3.193c{m}^3{s}^{-1};101.64cm{s}^{-1}$
• B. $3.193cm{s}^{-1};101.64c{m}^3{s}^{-1}$
• C. $3.193cm{s}^{-1};101.64cm{s}^{-1}$
• D. $31.93c{m}^3{s}^{-1};1016.4cm{s}^{-1}$

Answer 1

The correct option is A $3.193c{m}^3{s}^{-1};101.64cm{s}^{-1}$

From poiseuillis equ:
$Q=\frac{\pi r^4\Delta p}{8\eta L}$

$Q=\frac{\pi {10}^{-4\times {10}^4}}{8\times {10}^{-2}\times 1.23\times 10}$

$Q=\frac{10\pi }{8\times 1.23}c{m}^3/s$

$Q=3.1926c{m}^3/s\approx 3.193c{m}^3/s$

So, speed of liqued coming out $=\frac{10\pi \times 100}{8\times 1.23\times \pi \times {10}^{-2}}=\frac{1000}{8\times 1.23}cm/s$$=101.626cm/s$
$Q=3.193c{m}^3/s$
$v=101.64cm/s$