Question

A pipe of diameter $1.8m$ is required to transport an oil of specific gravity $0.90$ and viscosity $4\times {10}^{-2}$ poise at a rate of $3m^3/sec$. Test were conducted on a $18cm$ diameter pipe using water having viscosity $0.01$ poise. The velocity of flow in the model in $m/sec$. (round off to two decimals) is

• A. 2.64

Answer 1

The correct option is A 2.64
Given, $d_p=1.8m,{\mu }_p=4\times {10}^{-2}poise,Q_p=3m^3/sec$
$S_p=0.90$
For model
$S_m=1,{\mu }_m=0.01poise,d_m=0.18m$
For pipe flow, Reynolds model is applicable
$\frac{{\rho }_m{V}_m{d}_m}{{\mu }_m}=\frac{{\rho }_p{V}_p{d}_p}{{\mu }_p}$
$\frac{1000V_m\times 0.18}{0.01}=\frac{900V_p\times 1.8}{4\times {10}^{-2}}$
$V_m=2.25V_p$
$V_p=\frac{Q_p}{A_p}=\frac{3}{\frac{\pi }{4}\times (1.8{)}^2}=1.18m/sec$
$\therefore V_m=2.25\times 1.18$
$=2.655m/sec$.
$\approx 2.66m/sec$.