The Air Velocity In A Duct Is Measured By A Pitot-static Probe Connected To A Differential Pressure Gage. If The Air Is At 92 KPa Absolute And 20°C And The Reading Of The Differential Pressure Gage Is 1.0 KPa, Determine The Air Velocity.

Question-Answer › Category: Fluid Mechanics › The air velocity in a duct is measured by a Pitot-static probe connected to a differential pressure gage. If the air is at 92 kPa absolute and 20°C and the reading of the differential pressure gage is 1.0 kPa, determine the air velocity.

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John asked 4 months ago

The air velocity in a duct is measured by a Pitot-static probe connected to a differential pressure gage. If the air is at 92 kPa absolute and 20°C and the reading of the differential pressure gage is 1.0 kPa, determine the air velocity.

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Maweto Chito answered 4 months ago

Given,
Absolute pressure of Air (P) = 92 kPa
Absolute Temperature (T) = 20o C = 20+273 = 293 K
Differential Pressure gage (Pd) = 1.0 kPa

We can use ideal gas equation to find density of Air in duct
PV = mRT
P = ρRT ………(1) [  ρ = (m/V) ]
P = Absolute Pressure
  ρ = density
R = Characteristic Gas Constant
= 0.287 kJ/kg-K (for AIR)
T = Temperature in Kelvin
Putting the values in equation (1)
   $92 = \rho \times 0.287\times 293$
   $\rho =\frac{92}{0.287\times 293}$
$\mathbf{\rho =1.094 \: \, kg/m^{3}}$

For Pitot Static we know the Formula for velocity is
$V=\sqrt{2\times \frac{P_{d}}{\rho }}$ ……..(2)
V = Velocity of air in duct
  ρ = density of air
Pd = Differential pressure gage = 1.0 kPa = 1000 Pa
putting values in equation (2)
   $V=\sqrt{2\times \frac{1000}{1.094 }}$
$V=\sqrt{1828.1535}$
$V=42.756 \:$
$\mathbf{V=42.756 \: \approx 42.8\: m/s}$