course phy232
university physics problem (from test1)Basically, this problem just tells you to determine the velocity with which the water will exit from the hole in a uniform cylinder when the cylinder is filled to a point 3.1 meters above the hole, assuming that the water in the cylinder moves with negligible velocity.
I'm not going to go into extreme details, but wouldn't this just come to v2=sqrt(2gh). I know how to derive this, but don't feel like typing out all the details.
Your expression is correct.
You should use Bernoulli's Equation to get this, or alternatively use the reasoning by PE change.
But here's where I was a little unsure:
If the cylinder has a circular cross-section with radius 7 meters while the hole has a radius of .075 meters, then what is the total kinetic energy of the water in the cylinder above the hole.
Would you take your velocity that you found for the exit speed and apply it to the continuity equation? That's what I'm possibly thinking, then use it with 1/2 'rho v^2, to find the kinetic energy above the hole.
The continuity equation would give you the velocity of water in the cylinder; the radius and depth will give you the volume, from which you easily get the mass
It also asks you to explain why, if the hole is instantly unplugged, the exiting water will require a short time interval to reach its maximum velocity.
In a situation like this, wouldn't the fact that the distance between the hole of the cylindrial container which the water will exit and the point where the container has a uniform radius to the top of the cylinder have a pressure difference, and whenever the container is unplugged the water in that instant will flow out, but once the height starts to change, the water will have more pressure pushing down on it and will be able to achieve its maximum velocity.
It's good to understand that, but that doesn't answer this question.
One reason the change can't be instantaneous is Newton's Second Law. Speaking a bit loosely (this explanation would seem OK to a physicist but would drive a mathematician nuts), an instantaneous change in the velocity of anything implies infinite acceleration and would require infinite force.
Another consideration is that the water at the top of the cylinder doesn't know' that the hole has been unplugged until the pressure wave reaches it. The speed of the pressure wave is the speed of sound in water (sound is a pressure wave), which is high (in the thousands of meters per second) but still finite.
Hopefully that makes sense - honestly, I'm looking forward to getting this test completed and if I can take my calculus test next monday that would be great (I plan to complete my physics test probably the following tuesday).
Good plan.
See my notes.