A portable oxygen tank similar to one used in hospitals meas

A portable oxygen tank (similar to one used in hospitals) measures 30-cm-diameter and 1.3-m- high. The tank is pressurized to 13,800,000 Pa (gauge). A 12.5-mm-diameter valve is located at the top and when fully-opened, oxygen exits at a velocity of 1.5 m/s (25°C). Assuming a constant exit velocity, determine the pressure (in MPa gauge) after two minutes. Assume isothermal conditions.

Solution

Solution:-

Diameter of tank = 30 cm = 11.88 inch

Height of tank = 1.3 m = 51.18 inch

For above size of tank(cylinder)

Cylinder constant = 3.14

Gauge pressure = 13.8 *10⁶ Pa

1 Pa = 145.03 *10^-6 psi

Gauge pressure = 13.8*10⁶ *145.03*10^-6

Gauge pressure = 2001.414 psi

Residual pressure after 2 minute = ?

Velocity = 1.5 m/s

Flow rate = A*V

Flow rate = /4*(0.0125)² *1.5

Flow rate = 1.84 * 10^-4 m³/s

Flow rate = 11.04 L/m

We know that

((Gauge pressure - Residual pressure)/(flow rate in L/m)) * Cylinder constant = Duration of flow in minutes

((2001.414 - Residual pressure )/11.04 )* 3.14 = 2

Residual pressure = 1994.38 psi

Residual pressure after 2 minute = 13.75 MPa        Answer