Question

An ideal gas known as Minesium (MW=34.0) is flowing at a steady rate of 0.125 lbmol/min through a 62.5 in2 circular tube at a temperature of 185 °F and pressure of 42.0 psig. What is the velocity (ft/s) of this ideal gas? Assume Patm = 14.7 psia.

Answer 1

to calculate the velocity, we need to calculate the volumetric flow rate because velocity is volumentric flow rate divided by cross section area.

volumetric flow rate can be calculated using ideal gas equations.

PV = nRT (We will use equation in SI units fomat, we can use it any unit's format though)

Pabs = Pg+Patm = 42.0+14.7 = 56.7 psi; we know that 1 psi = 6895 Pa, so 56.7 psi = 56.7*6895 = 390933 Pa

n = 0.125 lbmol/min, we know that 1 lb = 453.6 gm and 1 min = 60 Sec, thus

0.125lbmol/min= 0.125*453.6/60 = 0.945 gmole/sec

R = 8.314 J/mol-k

T = 185 DegF

we know that temperature in K = 273 + (DegF-32)/1.8

T = 273+ (185-32)/1.8 = 358 K

PV = nRT

390933*V = 0.945*8.314*358

V = 7.195x10^-3 M3/sec = 7194.9 cm3/sec

tube cross sectionl area = 62.5 in2 since 1 in = 2.54 cm

area= 62.5 *2.54*2.54 = 403.2 cm2

velocity = volumetric flow rate/cross sectional area = 7194.9/403.2 = 17.84 cm/sec

now 1 cm = 0.0328 ft

thus velocity = 17.84*0.0328 = 0.586 ft/sec