A gas with a velocity of 300 m/s is flowing through a horizontal pipe at a section where pressure is 78 KN/m2 absolute and temperature 40°C. The pipe changes in diameter and at this section, the pressure is 117 kN/m2 absolute. Find the velocity of the gas at this section if the flow of the gas is adiabatic. Take R = 287 J/kg K and γ = 1.4.

Solution:

Section 1:

Velocity of the gas, $ V=300 \mathrm{~m} / \mathrm{s} \\ $

Pressure, $ p_{2}= 78 \mathrm{kN} / \mathrm{m}^{2} \\ $

Temperature, $ \quad T_{1}=40+273=313 \mathrm{~K} \\ $

Section 2 :

Pressure, $ p_{2}=117 \mathrm{kN} / \mathrm{m}^{2} \\ $

$ R=287 \mathrm{~J} / \mathrm{kg} \mathrm{K}, \gamma=1.4 \\ $ …