Help Deriving Trajectory of Water out of Pipe

[lukeseed]

I suppose this is also related to thrust vectors.

I have a Y pipe with two exit nozzles. These exit nozzles are angled 43.75 degrees from the vertical and are at a radius of .1968m from the vertical. These nozzles have a deflector that can move from 0 degrees (fully open), to 90 degrees (fully closed) [which would make the water angle move from 43.75 degrees when open to -46.25 degrees when fully closed.
These deflectors are mounted on collars which rotate around the pipe nozzle from angles 0 to 90 degrees.

I need to calculate the coverage area for all angles, deflector and collar rotation, with respect to various heights above a pool. I am having a real problem calculating the initial velocity vector and how that relates to a coverage radius. I am not currently worried about frictional or momentum loss in the fluid upon contact with the deflector. I guess this is mostly a geometry problem with a little bit of constant acceleration thrown in.

Anyone have any suggestions on finding the initial velocity vector of the water and how that relates to the final landing point?



Thanks,

 

[LightHero]

The answer to your question lies in the concept of thrust vectors. Thrust vectors refer to the force applied by the nozzle to the water as it exits, and the direction in which this force is applied. To calculate the coverage area for all angles and deflector/collar rotations, you will need to determine the initial velocity vector of the water and how this affects the final landing point. The easiest way to do this is to use Newton's second law of motion, which states that the acceleration of an object is equal to the sum of all the forces acting on it divided by its mass. In this case, the sum of all the forces acting on the water coming out of the nozzle can be calculated by adding up the thrust vector from the nozzle and any external forces, like gravity or air resistance. The mass of the water can then be calculated based on the volume of the water being expelled from the nozzle. Once you have the acceleration and mass of the water, you can then calculate the initial velocity vector and how this affects the final landing point. This will allow you to determine the coverage area for various heights above a pool.

 

[astrokreng]

I would approach this problem by first breaking it down into smaller components and using mathematical equations and principles to solve for the desired information.

Firstly, I would consider the basic principles of projectile motion. The initial velocity of the water can be calculated using the formula v = u + at, where v is the final velocity, u is the initial velocity, a is the acceleration, and t is the time. In this case, we know the angle of projection (43.75 degrees) and the initial height (height above the pool), so we can use trigonometric functions to find the initial velocity in the horizontal and vertical directions.

Next, I would take into account the deflector and collar rotation. This will affect the angle of projection and ultimately the trajectory of the water. By considering the angles and distances involved, we can use geometry and trigonometry to calculate the final landing point of the water.

It is also important to consider the effect of gravity on the water as it travels through the pipe and exits the nozzles. This can be accounted for by using the equations of motion for constant acceleration.

Finally, I would recommend conducting experiments to validate the calculations and to account for any factors that may have been overlooked. This could include measuring the actual initial velocity and trajectory of the water using high-speed cameras, and adjusting the calculations accordingly.

Overall, this problem can be solved by applying principles of physics and mathematics, and by carefully considering all variables and factors involved. I hope this helps in your quest to derive the trajectory of water out of your pipe.