Glitttt, if I have interpreted your question correctly, then with an equal head of water they will have an equal pressure acting upon each of the pipes. I’m not sure what you mean by a head of water at a 4 degree height, but here’s my best shot at an answer!
Assuming equal systems (equal length pipes, water heads etc…), the only difference being the exit pipe radius. The pipe with the smaller radius (and thus cross sectional area) would be flowing the fluid at a higher exit velocity, and the fluid would therefore travel a further distance away from the pipe exit before hitting the ground. (Think of putting your thumb over the end of a hose, the velocity increases and the flow travels further).
However if you compare the two systems in terms of two fluid particles leaving the pipe at the same time, they would also both hit the ground at the same time, just the particle from the system with the smaller exit diameter would land further away from the pipe exit. This is assuming there is no deviation of height between the two landing points, i.e. the ground is perfectly flat. This is much the same as Colins bullet example, they will both hit the floor at the same time.
The second part of your question requires a bit more information, it will depend on whether or not either of the flows are choked, the fluid itself – density would be useful, as would viscosity, the pipe length and its discharge coefficient should be sufficient to give a reasonable estimation.
David, you seem to have a better understanding of how or why gravity actually occurs than me, however you have explained gravity as an acceleration, but called it a force…?!
You state (and I quote):
“F = mg”
i.e. Force = mass * gravity
So if force is equal to mass times gravity, how can gravity actually be a force!? You have substituted a (for acceleration) with g (gravitational acceleration) i.e. gravity!
You are correct in stating that gravitational acceleration is not quite constant, due to the world being an ellipse I would stab as the reason. But for arguments sake it is recognised as a constant of 9.81 m/s^2 – units of which are acceleration. This ‘constant’ as im sure you know has been derived from the exact experiment I described in my previous post, knowing the distance an object is dropped from and timing how long it takes to hit the ground, then using the derivative of the distance with respect to time to calculate the velocity the object when it hit the ground, and the second derivative to work out its acceleration.
Two objects of different masses will accelerate to the ground at the same rate! Conduct the experiment yourself and you will find that you will come out with an answer of ~10m/s^2 (which is ballpark 9.81m/s^2) dependent upon the accuracy of your timing and your release mechanism for the two objects. The main difference between two objects of different masses, unless they are of the same shape is how their shape affects their aerodynamic properties and differences between the resisting drag force which squares with velocity.
If gravity (as a useful constant) was a force then we would all have the same force acting upon us and pushing us into the ground. We would all weigh the same. A tank and a feather would weigh the same (i.e. we would all be forced into the ground by the same force). This simply is not the case!
The force due to gravity (an acceleration) is the resultant of the mass of an object and gravitational acceleration. It varies between objects of different mass (living proof, put two different objects upon some weighing scales).
If gravity was a force then F = ma simply would not work, and it does, so gravity therefore cannot be a force, but there is a force ‘because’ of gravitational acceleration, it is just different for different masses and is therefore a variable and not useful in multiple calculations for differing applications.
My conclusion:
Gravity, as a useful constant is an acceleration.
Force due to constant gravitational acceleration differs between two objects of different masses, is therefore variable and cannot be denoted as ‘gravity’.
Chris
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Gravity...... by 'Newshound' (29 Dec 2010 @ 20:03)
