# Find the velocity of an airplane flying at a standard sea level, if the static pressure at the throat of venturi is $$100 000 N/m^{2}$$.

A venturi is attached on a side of an airplane fuselage, has an throat to inlet area ratio of $$0.8$$.  Find the velocity of an airplane flying at a standard sea level, if the static pressure at the throat of venturi is $$100000 N/m^{2}$$.

Asked on 15th June 2021 in

A venturi is a device which is used to measure the airspeed. It is a converging diverging duct. The inlet pressure and velocity of the duct is $$p_{1}$$ and $$v_{1}$$. At the throat of the duct velocity increases to the maximum, $$v_{2}$$ and pressure decrease to minimum, $$p_{2}$$. In the divergent section of the duct, velocity decreases and pressure increases. The inlet and throat area of the duct are $$A_{1}$$ and $$A_{2}$$.

A venturi

Velocity of air is calculated using Bernoulli’s equation, which is$v_{1}=\sqrt{\frac{2\left ( p_{1} – p_{2} \right )}{\rho \left [ \left ( \frac{A_{1}}{A_{2}} \right )^{2}-1\right ]}}$ Here, $$p_{1}$$ is the atmospheric pressure, which is $$101325\,N/m^{2}$$, $$p_{2}=100000\,N/m^{2}$$,$$\frac{A_{2}}{A_{1}} = 0.8$$.

On putting the values, $v_{1}=\sqrt{\frac{2\left ( 101325-100000 \right )}{1.225\left [ \left ( \frac{1}{0.8} \right )^{2}-1\right ]}}$$\Rightarrow v_{1}=62.015\,m/s$Therefore, velocity of the airplane is $$62.015\,m/s$$.