Question

A pitot tube system measures the static pressure in 50 cm diameter duct containing air (\rho\:=rho =1.1 kg/m3) as 97 kPa and the impact pressure as 100 kPa. What is the air velocity?

Answer 1

Answer:

The velocity in duct is 73.854 m/s.

Explanation:

Given that Pitot tube measuring velocity v in 50 cm diameter duct contain air of density 1.1 $\frac{kg}{m^{3} }$.

Also, P1 = Pressure in duct is 97kpa and P2 = Pressure at impact or stagnation point is 100kpa.

Using Bernoulli equation,

$P+\frac{1}{2}\rho v^{2} +\rho gh=0$

When air is flowing through duct,

$97,000+\frac{1}{2}\rho v^{2} +\rho gh1=0$

When air is at stagnation point.

$1,00,000+0+\rho gh1=0$

Comparing both the equation,

$97,000+\frac{1}{2}\rho v^{2} +\rho gh1=1,00,000+\rho gh1$

$\frac{1}{2}\rho v^{2}=3000$

$0.55v^{2}=3000$

$v^{2}=5454.54$

v=73.854 m/s.

Therefore, The velocity in duct is 73.854 m/s.