Question

Nitrogen is fed from a high pressure cylinder, through 1/4 inch ID stainless steel tubing, to an experimental unit. The line ruptures at a point 10 ft from the cylinder. If the pressure of the nitrogen in the cylinder is 2200 psig and the temperature is 70°C

a) Use the ideal gas law to calculate the density of gas in the tank

b) What is the mass flow rate of the gas through the line?

c) Is the flow choked?

d) What is the pressure in the tube at the point of the break? Solve parts b-d as graphical case D problem

e) Solve as a Type II incompressible flow problem using the incompressible flow MEB, and keep the ?P/?, ?F, and ?KE terms in the balance. Compare to the compressible flow calculation.

Answer 1

(a) Ideal gas law: PV = nRT = mRT/M_w (P = absolute pressure, V = Volume, n = moles, m = Mass, R = Gas constant, T = absolute temp., Mw = Molecular weight.

Density = M/V =    

Convert all the quantities in SI unit system:

P_abs = (2200 + 14.7 )psig = 2214.7 psig = 15269819 Pa

M_w = 0.028 kg/mol, R = 8.314 J/mol.K , T = 70 + 273.15 = 343.15

Density of gas in tank = 149.8642 kg/m³

(b) Area of tube = ? ID² = 3.14 (0.25)² = 0.19625 inch² = 0.000126 m²

Mass flow = density*area = 0.018975 kg/m

If velocity is known mass rate = 0.018975 * velocity =.... kg/s.

(c) Flow is not choked.

(d) Pressure drop along the pipe = Length x density x velocity² / (2 x Diameter).

Velocity needs to be known . Pressure at break = 2200 psig - pressure drop.