Consider a self-contained underwater breathing apparatus (SCUBA) diving tank with a volume of
18 litres and a maximum pressure rating of 200 bar (gauge). The tank can be pressurized to this 200
bar pressure limit. Before diving, the tank should be filled with air via a compressor, capable of
delivering air at a 4.2 ft3/min flow rate. The valve, through which air enters (or leaves) the tank, has
a throat diameter of 12 mm.
The tank is to be filled on a nice sunny day, when the temperature is 30°C and the atmospheric
pressure is 102 kPa. For simplicity, you may assume that while filling the tank the temperature
throughout the compressor, the feed lines and the tank remains uniform and equal to the ambient
temperature of 30OC.
Note that the universal gas constant for air is R = 287.053 J/kg/K.
Your task is to determine various details of the filling and discharging of the tank, namely:
(1) Determine the mass of air (in terms of kg units) inside the tank just before the filling process
begins. You may assume at the beginning that the pressure inside the tank is equal to the
(2) In order to be able to pressurize the tank to 200 bar (gauge), what should be the compressor outlet
pressure? Please select one answer from the choices below:
V = 18 L
D = 12 mm
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(b) Between vacuum and atmospheric pressure
(c) Between atmospheric pressure and 200 bar (gauge)
(d)Higher or equal to 200 bar (gauge)
(3) Determine the amount of air (again, in terms of kg units) to be pumped into the tank so that the
tank pressure reaches 200 bar (gauge). Note: This should be the amount of air to be pumped into
the tank on top of what you have already calculated in part (1) above.
(4) Determine the time required to fill the tank. You may assume that the compressor’s given flow
rate refers to air density corresponding to atmospheric conditions.
(5) Now that the tank is filled, it can be used for SCUBA diving. For this, air is discharged from the
tank through the same valve used for filling the tank. Assuming that the air outflow velocity through
the valve throat is a constant 0.1 m/s throughout the discharge (i.e. roughly the rate at which we
breathe), and considering that the density and pressure in the tank drops continuously in time (i.e. Ptank = f(t)) , then determine the time required to reduce the air density in the tank by 90%.
Hint: This is an unsteady problem. You may assume that the mass flow rate through the valve can
be expressed as dm/dt=C*Ptank(t)where C is a constant and Ptank(t)is the instantaneous
density inside the tank..
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