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

The velocity in duct is 73.854 m/s.

Step-by-step explanation:

Given that Pitot tube measuring velocity v in 50 cm diameter duct contain air of density 1.1
`(kg)/(m^(3) )`.

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

Using Bernoulli equation,

`P+(1)/(2)\rho v^(2) +\rho gh=0`

When air is flowing through duct,

`97,000+(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+(1)/(2)\rho v^(2) +\rho gh1=1,00,000+\rho gh1`

`(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.