Calculation for inflation time of an air bladder?

[IPFWengineer]

Hi,

I was curious if you could help me. I am currently working on a project where we are using 12g CO2 cylinders to fill an expanable air bladder to absorb impacts like an air bag. I am having trouble though calculating how long it would take to inflate the bladder with known variables:

-Given-
-CO2 canister pressure = 858psi
-Orfice diamerter = 0.028"
-Expanded bladder volume = 1317 in^3
-Final bladder pressure = 2psi

We are using three cylinders to inflate the bladder along with each having their own puncture pin with orfice size given.

Any help would be greatly appriciated.

Regards,
Chris

 

[eljose79]

Dear Chris,

Thank you for reaching out for assistance with your project. I would be happy to help you calculate the inflation time for your expanable air bladder.

First, we need to determine the total volume of CO2 available from the three cylinders. Since each cylinder has a pressure of 858psi and the orfice diameter is 0.028", we can use the ideal gas law to calculate the volume of CO2 in each cylinder:

V = nRT/P

Where:
V = volume of gas (in liters)
n = number of moles of gas
R = gas constant (0.0821 L·atm/mol·K)
T = temperature (in Kelvin)
P = pressure (in atm)

Converting the pressure to atm and assuming room temperature of 298K, we get:

V = (n * 0.0821 * 298) / (858/14.7)
V = (n * 24.44) / 58.41
V = 0.418 * n

Since we have three cylinders, the total volume of CO2 available is:

Vtotal = 0.418 * 3 * n
Vtotal = 1.254 * n

Next, we need to calculate the flow rate of CO2 through the orfice. This can be done using the Bernoulli's equation:

P1 + 1/2ρv1^2 + ρgh1 = P2 + 1/2ρv2^2 + ρgh2

Where:
P1 = initial pressure (858psi)
ρ = density of CO2 (1.977 kg/m^3)
v1 = initial velocity (unknown)
P2 = final pressure (2psi)
v2 = final velocity (unknown)

Since the bladder is expanding, we can assume that the final velocity (v2) is close to zero. Therefore, the equation becomes:

P1 + 1/2ρv1^2 = P2

Solving for v1, we get:

v1 = √((2*(P1-P2))/ρ)
v1 = √((2*(858-2))/1.977)
v1 = √(433.5)
v1 = 20.82 m/s

Now, we can calculate the flow rate (Q) through the orfice using the equation:

Q = Av1

Where: