Gas pressure question

Dan Moskal

I have a couple related questions that I need your help to answer, I couldn't find the answer in any engineering manual. Sorry if I went into too much detail but I figure it's better to give you too much info than too little.

The two related questions regarding the physics of a gas moving between vessels with different pressure levels. In both cases we have two vessels connected by a pipe. One vessel is at 1 atmosphere pressure (101.3 kN/m2 or 14.7 lb/in2) and the other at 10 atmospheres pressure (1013 kN/m2 or 147 lb/in2). The gas used is uniform air with a density of 1.229 kg/m3 or .00237 slug/ft3 at one atmosphere pressure and a density of 12.29 kg/m3 or .0237slug/ft3 at 10 atmospheres pressure.

The questions are these. 1) The pipe between the vessels is opened up so 1/10 of a cubic meter of gas (weighing 1.229 kg or 2.704 lbs) at 10 atmospheres pressure is sucked into the vessel at one atmosphere pressure. The gas in the pipe stays at 10 atmospheres pressure until it enters the lower pressure vessel. The gas will move with considerable speed and force down the pipe as it travels to the lower pressure vessel. The question is this, how much total force is exerted by the blowing gas in the pipe? (I am not asking how much force there is when the gas expands in the lower pressure vessel, although I am curious to know that too.) Assume that as the gas enters the lower pressure vessel and equal mass of gas is drawn out from a separate pipe so the pressure remains at 1 atmosphere. Also ignore friction losses. 2) You have the same two vessels, but this time there is a one-way air valve separating them. Now we want to force 1 cubic meter of gas (weighing 1.229 kg or 2.704 lbs) at one atmosphere pressure into the vessel, which is at 10 atmospheres pressure. The gas stays at 1 atmosphere pressure until it is past the one-way air valve and into the higher pressure vessel. The question is this, how much total force (the force is in the form of a strong blowing wind) will have to be applied to the gas to get it past the one-way air valve? (I am not asking how much force is needed to compress the gas once it is in the vessel, only how much force is needed to get it past the valve.) Assume as the gas enters the higher pressure vessel and equal mass of gas is drawn out from a separate pipe so the pressure remains at 10 atmospheres. Also ignore friction losses.

I know the amount of force needed to compress gas is equal to the amount of force released when the gas expands (ignoring friction losses). Is the amount of force needed to get the gas past the one-way air valve into the higher pressure chamber the same as the amount of force of the blowing gas in the pipe has when it is sucked from the higher pressure vessel into the lower pressure one (ignoring friction losses)? The weight of the gas in both examples is the same, but the volume of lower pressure gas going past the valve is 10 times the volume of the high pressure gas going through the pipe. Does the volume effect the amount of force needed or does the mass alone matter?

Thank you for your help.