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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-AnswerCategory: Fluid MechanicsThe 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.
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.

1 Answers
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}

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