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 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 $62.015\,m/s$.