The pressure leads from Pitot-static tube mounted on an aircraft were connected to a pressure gauge in the cockpit. The dial of the pressure gauge is calibrated to readthe aircraft speed in m/s. The calibration is done on the ground by applying a known pressure across the gauge and calculating the equivalent velocity using incompressible Bernoulli’s equation and assuming that the density is $1.224 kg/m3$.

The gauge having been calibrated in this way the aircraft is flown at $9200 m$, where the density is $0.454 kg/m3 $and ambient pressure is $30 kN/m2$. The gauge indicates a velocity of $152 m/s$. What is the true speed of the aircraft ?

(UPSC exam)

Solution:

Bernoulli's equation for an incompressible flow is given by,

$$ p+\frac{\rho V^{2}}{2}=\text { constant } \\ $$

The stagnation pressure $\left(p_{s}\right)$ created at Pitot-static tube,

$$ p_{s}=p_{0}+\frac{\rho_{0} V_{0}^{2}}{2} \text { (neglecting compressibility effects) }...(1) \ $$ $$ p_{0}=30 \mathrm{kN} / \mathrm{m}^{2}, V_{0}=152 \mathrm{~m} / \mathrm{s}, \rho_{0}=1.224 \mathrm{~kg} / \mathrm{m}^{3} …