Question

A rotameter with a heavy float of density ${\rho }_f$ is used for mesuring gas flow is calibrated with a gas of density $\left(\rho \right)1.5kg/m^3$. If it measures the flow rate of a different gas having density of $2kg/m^3$ and indicates a flow rate of $10m^3/min$. The actual flow rate is ________ $m^3/min.$ $\text{(Assume}{\rho }_f>>\rho )$

• A. $10m^3/min$
• B. $20m^3/min$
• C. $5m^3/min$
• D. $11.5m^3/min$

Answer 1

The correct option is D $11.5m^3/min$

Equation for volume flow rate of rotameter is,

$Q=\frac{C_d(A_t-A_f)}{\sqrt{1-{(A_t-A_f)}^2/A_t^2}}\cdot \sqrt{\frac{2g{V}_f({\rho }_f-\rho )}{\rho .A_f}}$

$\text{As}{C}_d,A_t,A_f,V_f\text{are constant.}$

$\therefore {\rho }_f>>\rho$

$\therefore {\rho }_f-\rho \approx {\rho }_f$

$So,Q=\sqrt{\frac{{\rho }_f}{\rho }}$

$\frac{Q_1}{Q_2}=\sqrt{\frac{{\rho }_2}{{\rho }_1}}[\because {\rho }_f=constant]$

So,

$Q_1=Q_2\sqrt{\frac{{\rho }_2}{{\rho }_1}}=10\sqrt{\frac{2}{1.5}}=11.5m^3/min$