292m. This length will allow us to get the maximum expansion from the beginning pressure and expel all the water.
.
Bernoulli Equation.
Assumptions:.
• Travels horizontal.
• Piston starts at complete rest.
• Pressure is exactly at 344.750kPa.
• Cylinder is frictionless with piston.
• Invicid flow.
• Incompressible fluids.
Using:.
.
• V1 goes to zero because piston is at rest when time is at zero.
• Z1 and Z2 go to zero because we are neglecting gravity forces.
We find:.
Solving for V2.
.
Therefore, we discover that using the Bernoulli equation, the exit velocity is 22.08m/s. .
Mass Flow Rate.
Assumptions: .
• Piston starts from rest.
• Pressure is exactly at 344.750kPa.
• Water and air are at 20 degrees Celsius.
Using:.
.
• Using Vexit from the Bernoulli analysis.
We find:.
.
Therefore, we find that by using mass flow rate equals the density of the fluid times the exit velocity times the area of the tube, mass flow rate out of the submarine is 0.4326kg/s.
Burn Time.
Assumptions: .
• The only mass exiting is the water.
Using: .
.
• Using the mass flow rate from previous analysis.
.
We find:.
.
Therefore, the only change in mass is the change in mass of the water leaving. Using the equation, mass flow rate out is equal to the change in mass over the change in time, we get that the change in time is 1.734seconds.
.
Conservation of Momentum.
Assumptions:.
• Deceleration is constant.
• Exit velocity is constant.
• Neglect all drag.
• No sloshing.
• mo = 2.266 kg.
Using: .
.
First term:.
This term goes away because we neglected drag.
Second term: .
.
Third term:.
.
Therefore the equation goes to:.
.
We find:.
.
Therefore, using the change in momentum equation, we find that the submarine will travel 10.633m/s in the water, analyzed according to our assumptions.