Discharging of a cylinder (control volume Analysis)

Consider a tank containing a gas at known conditions of temperature and pressure (figure 15.2).

Figure 15.2

The valve is opened, the gas escapes from the tank and the properties of the gas in the tank change with respect to time.

Let, pressure of the gas inside the cylinder at

temperature of the gas inside the cylinder at

specific internal energy of the gas inside the cylinder at

and denote corresponding quantities of the gas left in the cylinder after the discharging operation.

velocity of the escaping gas. From the first law, we can write

(15.12)

No material flows into the cylinder and the potential energy changes can be ignored. Then

(15.13)

For the discharging process, the conservation of mass gives

(15.14)

Integrating the above equation over time gives

(15.15)

Integration of the governing equation yields

(15.16)

Now the term on the left hand side may be evaluated as

(15.17)

Similarly,

(15.18)

and

(15.19)

Finally invoking (15.17), (15.18) and (15.19) in (15.16) we get

(15.20)

It is assumed that the gas escapes with a uniform velocity V and specific enthalpy h.