Question

A rigid tank having 21.225 m^3 volume contains air having density of 1.829 kg/m^3 Air is supplied to the tank from a high-pressure supply line via a valve connection, until the air density reaches to 5.007 kg/m^3. This procedure has taken 56.101 minutes. Calculate the mass flow rate of the air supplied from high- pressure line to the tank. Enter your result in kg/s, and use 3 decimals.

Answer 1

0.020 Kg/s

Step-by-step explanation:

Given:

Volume of the rigid tank, V = 21.225 m³

Initial density of the air, ρ₁ = 1.829 Kg/m³

Final density of the air, ρ₂ = 5.007 Kg/m³

Total time for the procedure, t = 56.101 minutes = 56.101 × 60 = 3366.06 s

Now,

Mass = Density × volume

thus,

Initial mass of the air in the tank = ρ₁ × V = 1.829 × 21.225 = 38.820 Kg

Final mass of the air in the tank = ρ₂ × V = 5.007 × 21.225 = 106.273 kg

Therefore,

Total mass inflow in the tank = Final mass of the air - Initial mass of the air

or

Total mass inflow in the tank = 106.273 - 38.820 = 67.453 Kg

hence,

the mass flow rate = Mass inflow / Time

or

The mass flow rate = 67.453 Kg / 3366.06 s = 0.020 Kg/s