Question

Air flows into a pipe at a volume flow rate of 0.5m³/s and a speed of 1.0m/s. The temperature is tripled during the passage through the pipe and the pressure is doubled. What is the volume flow rate at the exit in standard SI units? [SHOW WORKING ]

Answer 1

Since input mass rate ( total mass of air entering the pipe per unit time) = output mass rate ( total mass of air leaving the pipe per unit time)

Mass rate = volume rate * density

Now , we know

From ideal gas equation

PM = dRT , P is pressure , M is molecular weight of gas/air( which is constant) , d is density , T is temperature

d = PM/RT

Now , when P becomes double , T becomes Triple

Then as per above equation

Density d becomes = 2/3 of initial density

If density of incoming air is d

Then density of outgoing air = 2d/3

So ,

V1 * d1 = V2*d2 , (mass flow rate same)

0.5 * d = V2 * (2d/3)

V2 = 0.75 m^3/s

Volume rate at exit = 0.75 ,Answer