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Fluid Dynamics

            
             We, have worked this assignment entirely on our own and have received help from no one outside of our group.
             Our design consists of a piston-cylinder mechanism that expels water out to produce propulsion. A valve stem allows us to compress air in the air chamber. We will be able to find a volume of air which will maximize the expansion therefore maximizing the use of water for propulsion. We will also be able to calculate the buoyancy force acting on the design itself. By counteracting this force, it will allow us to create a submerged craft. By making assumptions, we can use Bernoulli's equation to determine the exit velocity from the craft. Using this exit velocity we determine the mass flow rate out of the valve. With this information and the change in mass, we can determine the burn time, allowing us to use the momentum equation to calculate the average velocity of the craft. Predicting the burn time and the average velocity will enable us to find the distance the craft traveled in the water. .
             Our submarine design consists of a piston-cylinder mechanism. Compressed air on the valve stem side forces the piston to expel water out the nozzle side resulting in propulsion.
             Buoyancy Force.
             Assumptions: .
            
             • Water is at 20 degrees Celsius .
            
             • Air is at 20 degrees Celsius and 101.325kPa.
            
             • Neglect volume of nozzle and valve stem.
             Using:.
             = .
             .
             .
             .
             We find:.
             .
             .
             Therefore, when the submarine is in 20 degree water with its calculated volume, the buoyancy force acting on it is 19.2N in the positive y direction.
             Maximum Compressed Air Expansion.
             Using P1V1 = P2V2, we determine the initial volume of air which will allow all the water to be used for propulsion.
             Assumptions:.
            
             • Pressure in air chamber is exactly 344.750kPa.
            
             • h = 0.1524m.
            
             • Neglect friction of the piston.
             Using:.
             .
             .
             We Find:.
             .
             Therefore, using a given pressure, we determined the length from the top of the position of the piston should be to 0.


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