Engineers are designing a cylindrical air tank and are trying to determine the dimensions of the tank. The proposed material for the tank is rated to withstand an absolute pressure of 20 MPa at a temperature of 10˚C. If the tank is sized to have a diameter of 200 mm and hold 4.64 kg of air, what must the length of the tank be?

The length of tank is found to be 0.6 m or 600 mm

Explanation:

In order to determine the length, we need to find a volume for the tank.

For this purpose, we use ideal gas equation:

PV = nRT

n = no. of moles = m/M

Therefore,

PV = (m/M) (RT)

V = (mRT) / (MP)

where,

V = volume of air = volume of container

m = mass of air = 4.64 kg

R = General Gas Constant = 8.314 J/mol. k

T = temperature of air = 10°C + 273 = 283 K

M = molecular mass of air = 0.02897 kg/mol

P = Pressure of Air = 20 MPa = 20 x 10^6 N/m²

V = (4.64 kg) (8.314 J/mol. k) (283 k) / (0.02897 kg/mol) (20 x 10^6 N/m²)

V = 0.01884 m³

Now, the volume of cylindrical tank is given as:

V = 0.01884 m³ = π (Diameter/2) ² (Length)

Length = (0.01884 m³) (4) / π (0.2 m) ²

Length = 0.6 m = 600 mm