a projectile 20ft in lentgh 4-6 thousand lbs traveling @ 100mph @ 100ft below water surface can be stopped and/or have said projectile change its course by using how many pounds of water preasuure to achieve goal? And what are the approximate dimensions of water preassure needed for same.....

To determine the amount of water pressure required to stop or change the course of a projectile traveling under water, we can use the principles of fluid dynamics. We'll assume the projectile is cylindrical in shape.

1. Calculate the volume of the projectile:
The volume of a cylinder is given by the equation V = π * r^2 * h, where r is the radius and h is the height (length) of the cylinder. Since the projectile's length is given as 20ft, we need to find the radius.

Assuming a cylindrical shape, there are infinite possible radii, so we'll consider a few different options. Let's calculate for the minimum, intermediate, and maximum radius sizes within the given range of 4-6 thousand lbs, and take the average of the results obtained.

Minimum radius (4,000 lbs):
Mass of the projectile = 4,000 lbs = ρ * V * g
Mass per unit volume (density) of water, ρ = 62.4 lb/ft^3 (approx.)
Acceleration due to gravity, g = 32.2 ft/s^2
V = (4,000 lbs) / (ρ * g) = (4,000 lbs) / (62.4 lb/ft^3 * 32.2 ft/s^2)

Intermediate radius (5,000 lbs):
Do the same calculation as above using 5,000 lbs.

Maximum radius (6,000 lbs):
Do the same calculation as above using 6,000 lbs.

Average the radii obtained from the three calculations.

2. Calculate the required water pressure:
The pressure required to stop the projectile or change its course can be calculated by considering the change in momentum.

Momentum = mass * velocity
Change in momentum = (Projectile mass) * (Projectile velocity)

The force required to stop the projectile can be calculated as:
Force = change in momentum / time

Since time is not provided, we can assume an instantaneous action, allowing for a maximum force to be required.

Pressure = Force / Area
Area = π * r^2 (cross-sectional area of the projectile)

Calculate the pressure for each radius and then take the average.

3. Determine the approximate dimensions of water pressure needed.
Once we have calculated the required water pressure, we need to find the dimensions that can generate this pressure. However, without knowing the shape of the object that will exert the force on the projectile, it is difficult to determine the dimensions accurately. The shape and design of the force-generating object will have a significant impact on the dimensions needed to achieve the desired water pressure.

It's important to note that the calculations provided above are based on assumptions and approximations. In practical applications, professional engineers and experts should be consulted to ensure accurate and safe mechanisms for stopping or changing the course of high-velocity projectiles underwater.