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Please post this type of questions in the HW section using the template.

Hello, I was curious about how to calculate how fast the escape velocity of hydrogen out of a tube/cylinder would be. Once end of the cylinder is closed, the other is open, obviously.

Assume the cylinder is full of hydrogen at 1 atm. My thought is that you could use PV=NRT to calculate the volume of the hydrogen once combusted and then imagine a sphere that had that equivalent volume. Online i found that the max flame speed of hydrogen is 3.06 m/s. I think you could start from the center of the sphere and calculate how long it would take to fill that volume if you went out radially at that speed(radius/3.06 m/s). Take the volume and divide it by the time to get the rate.

Once you have that rate, you could take the rate of the combustion (Vol/sec) and divide that by the volume of the cylinder to get the multiple. For example: if the rate of combustion is 1000L/sec and the cylinder is 1 L, then the gas will expand to 1000x the volume of the cylinder in 1 second. By multiplying the length * the multiple(1000) and dividing by 1 second, that would give a decent approximation for the escape velocity of the gas coming out of the tube. Them multiplying that by the mass/sec (flow rate) gives you the thrust.

Does this seem reasonable? Or is there an equation i can use for this.

Assume the cylinder is full of hydrogen at 1 atm. My thought is that you could use PV=NRT to calculate the volume of the hydrogen once combusted and then imagine a sphere that had that equivalent volume. Online i found that the max flame speed of hydrogen is 3.06 m/s. I think you could start from the center of the sphere and calculate how long it would take to fill that volume if you went out radially at that speed(radius/3.06 m/s). Take the volume and divide it by the time to get the rate.

Once you have that rate, you could take the rate of the combustion (Vol/sec) and divide that by the volume of the cylinder to get the multiple. For example: if the rate of combustion is 1000L/sec and the cylinder is 1 L, then the gas will expand to 1000x the volume of the cylinder in 1 second. By multiplying the length * the multiple(1000) and dividing by 1 second, that would give a decent approximation for the escape velocity of the gas coming out of the tube. Them multiplying that by the mass/sec (flow rate) gives you the thrust.

Does this seem reasonable? Or is there an equation i can use for this.