Question

In order to estimate the energy loss in a pipeline of 1 m diameter through which kerosene of specific gravity 0.80 and dynamic viscosity 0.02 poise is to be transported at the rate of 1 $m^3/s$, model tests were conducted on a 0.1 m diameter pipe using water at ${20}^{\circ }C$ is 1.00 $\times {10}^{-2}$ Poise, then the discharge required for the model pipe would be

• A. $60l/s$
• B. $80l/s$
• C. $120l/s$
• D. $160l/s$

Answer 1

The correct option is B $80l/s$

For dynamic similarity, Reynolds model law will be used.
$\frac{{\rho }_p{V}_p{L}_p}{{\mu }_p}=\frac{{\rho }_m{V}_m{L}_m}{{\mu }_m}\Rightarrow \frac{0.8\times {\rho }_w\times Q_p\times 1}{A_p\times 2\times {10}^{-2}}=\frac{{\rho }_w\times Q_m\times 0.1}{A_m\times 1\times {10}^{-2}}\Rightarrow Q_m=\frac{0.8\times 1\times \frac{\pi }{4}(0.1{)}^2\times 2}{\frac{\pi }{4}\times 1^2\times 2\times 0.1}\Rightarrow Q=0.08m^3/sec=80l/sec.$