A gas flows into a rigid container

[radwa]

A gas flows into a rigid container...

hi
will somebody please help me to solve this question;
A gas flows into a rigid container initially evacuated.Assume that the inflow velocity is uniform at 2m/sec.The tube inlet diameter is 10cm with the volume of the tank equal to 2000(litres). The pressure and temperature in the inlet line are maintained constant at 400 kPa
and 330k respectively. The gas can be assumed to obey the perfect gas law P=ρRT, with R = 300 J/Kg.K. Assume the tank to be non-insulated so that the temperature of the gas remains constant at the room temperature of 300 K. Determine,
The rate of change of the gas density inside the tank, and the time required for the pressure in the tank to reach 300 KPa

 

[Aaron Barnard]

The rate of change in the gas density inside the tank is given by:

-dρ/dt = (P1 - P2)/(V1*R*T)

where P1 and P2 are the pressures at the inlet and outlet respectively, V1 is the volume of the tank, R is the ideal gas constant, and T is the temperature of the gas.

Substituting the given values, we get:

-dρ/dt = (400 - 300)/(2000*300*300)

-dρ/dt = 0.00111 Kg/m3/s

The time required for the pressure in the tank to reach 300 KPa can be calculated using the following equation:

t = (P1 - P2)*V1/(Q*R*T)

where Q is the flow rate of the gas.

Substituting the given values, we get:

t = (400 - 300)*2000/(2*300*300)

t = 8.33 s