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## Q. 6.P.20

A gas of molecular weight 44 kg/kmol, temperature 373 K and pressure 202.6 kN/m² is flowing in a duct. A pitot tube is located at the centre of the duct and is connected to a differential manometer containing water. If the differential reading is 38.1 mm water, what is the velocity at the centre of the duct?
The volume occupied by 1 kmol at 273 K and 101.3 kN/m² is 22.4 m³.

## Verified Solution

As shown in section 6.2.5, for a pitot tube:

$u_1^2 / 2+P_1 v=u_2^2 / 2+P_2 v$

$u_2=0$, and hence, $u_1=\sqrt{2\left(P_2-P_1\right) v}$

Difference in head = 38.1 mm of water

$P_2-P_1=((38.1 / 1000) \times 1000 \times 9.81)=373.8 N / m ^2$

The specific volume, $v=(22.4 / 44)(373 / 273)(101.3 / 202.6)=0.348 m ^3 / kg$

∴                       $u_1=\sqrt{2 \times 373.8 \times 0.348}=\underline{\underline{16.1 m / s }}$