Calculating distance a water jet sprays before hitting ground

Captain Slow IRL

As the title says, I'm looking for an equation that calculates how far I can shoot water from a garden hose before gravity takes over and it hits the ground? Is the resultant the sum of the force in the water and gravity? (ignoring wind resistance)

fly_agaric

Captain Slow IRL wrote: »

As the title says, I'm looking for an equation that calculates how far I can shoot water from a garden hose before gravity takes over and it hits the ground? Is the resultant the sum of the force in the water and gravity? (ignoring wind resistance)

If you neglect air resistance the only force is gravity so it becomes a simple enough ballistics problem (I'm sure google can give the equations for range of a projectile etc).
You would need to know speed of the water jet leaving the hose head, height it is off the ground and the angle hose makes with the ground to get the distance.

Captain Slow IRL

I got a formula off this page: http://hyperphysics.phy-astr.gsu.edu/hbase/traj.html#tra2 for horizontal trajectory, stuck what I know into it and think I got what I was looking for!

I have velocity, angle and height off the ground.

Another question; for the continuity equation, Q=v.a, is Q the constant value?

Maximus Alexander

Captain Slow IRL wrote: »

As the title says, I'm looking for an equation that calculates how far I can shoot water from a garden hose before gravity takes over and it hits the ground? Is the resultant the sum of the force in the water and gravity? (ignoring wind resistance)

I would approximate this as follows:

d = 1/2 gt^2 tells us the distance travelled (d) for a body falling for time (t) in standard gravity (g).

We want to solve for time, so swap that around to sqrt(2d/g) = t

So, let's say your hose is a meter off the ground and perfectly horizontal, that gives us:

sqrt( 2 / 9.80665 ) = t = 0.451 s

That's how long it takes water droplets leaving your hose to hit the ground. Now you just need to know their horizontal speed leaving the nozzle in order to figure out how far they'll go.

fly_agaric

Captain Slow IRL wrote: »

I got a formula off this page: http://hyperphysics.phy-astr.gsu.edu/hbase/traj.html#tra2 for horizontal trajectory, stuck what I know into it and think I got what I was looking for!

I have velocity, angle and height off the ground.

Another question; for the continuity equation, Q=v.a, is Q the constant value?

If you mean what I think you mean there (edit: didn't make the connection immediately!) Q is just the flow rate through your hose system (volume of water per unit time) (which would be constant). (edit: Also "where will it land" part of that page looks like it will do what you needed (or above short cut)).

FISMA.

Captain Slow IRL wrote: »

As the title says, I'm looking for an equation that calculates how far I can shoot water from a garden hose before gravity takes over and it hits the ground? Is the resultant the sum of the force in the water and gravity? (ignoring wind resistance)

Is this for a real life application or paper? Are you familiar with the kinematic equations or the law of conservation of energy. Either will work.

If you measure how high the water goes, we can give you a nice idea of your muzzle velocity. If you know the muzzle velocity it would be easy to determine roughly how far the water would go for a certain angle.

Captain Slow IRL

It was just for on paper.

I wasn't able to accurately measure the diameter of the water outlet at the time.