Dynamics Question (water falling from the side of a tank)

In summary, the conversation discusses the dynamics of water falling from a tank with a hole in the side. The problem is solved using equations for projectile motion and accelerated motion, and the initial speed of the water is found to be a function of the height of the hole. The conversation also mentions that the water can be considered to come in "bullets" rather than continuously.
  • #1
CloudDreamer7
4
0
[SOLVED] Dynamics Question (water falling from the side of a tank)

Homework Statement


A large tank rests on the ground and has a water level 10 m above the ground. Water issues from a small hole in the side, 1 m below the the surface of the water. How far from the side of the tank will the water hit the ground ? Is there another height at which if a hole were drilled there, the water from it would reach the ground at the same point? Justify ur answer.



The Attempt at a Solution


as every logical person i assumed that water falls in projectile manner so on the x -axis you have x = v(x)t where x is the position where the water hits the ground, v(x) is the x-component of velocity and t is time; on the y-axis you have accelerated motion and so you have 2 eqns :

y = y0 + 1/2 gt^2 and t = v(y)/g

where v(y) is the y - component of velocity, y is the height, and y0 is the starting point.

i found the time t from here but i fail to go any further because i don't know how to get v(x) or sth that can help me find v(x).

Now this might not seem like an undergraduate problem but i am in 2nd yr and we are having sth like a general physics paper as a revision kinda thing. so this is in reality 1st yr dynamics staff. And its weird that i can't solved it because i used to be good in these. *sigh*
 
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  • #2
Assume that the water issues from the hole horizontally.

Hints: Find the initial speed as a function of hole height (h). Then try to find the horizontal distance as a function of h.
 
  • #3
Welcome to PF!

CloudDreamer7 said:
A large tank rests on the ground and has a water level 10 m above the ground. Water issues from a small hole in the side, 1 m below the the surface of the water.

Hi CloudDreamer7! Welcome to PF! :smile:

It can't make any difference whether there's a great big tank or just a curved pipe which finishes horizontally and which happens to be 1m from top to horizontal outlet.

In steady flow, I think it doesn't make any difference whether the water comes continuously, or comes in "bullets".

So work out the kinetic energy for a bullet of water falling 1m. :smile:
 

1. How does the shape of the tank affect the dynamics of water falling from the side?

The shape of the tank can affect the dynamics of water falling from the side in a few ways. If the tank has a wider opening, the water will spread out more as it falls, creating a wider and potentially more chaotic splash. If the tank has a narrower opening, the water will be more focused and create a smaller splash. Additionally, the shape of the tank can affect the flow of water as it falls, causing it to curve or twist in different ways.

2. What factors influence the rate at which the water falls from the tank?

The rate at which the water falls from the tank can be influenced by a few different factors. The height of the tank, the amount of water in the tank, and the size of the opening at the bottom of the tank can all impact the speed at which the water falls. The viscosity of the water and any external forces, such as wind, can also affect the rate of falling.

3. How does the temperature of the water impact the dynamics of its fall from the tank?

The temperature of the water can impact the dynamics of its fall from the tank in a few ways. If the water is warmer, it may have less surface tension and therefore create a wider splash as it falls. Cold water, on the other hand, may have a higher surface tension and create a more focused and smaller splash. Additionally, the temperature can affect the density of the water, which can impact its overall flow and speed as it falls.

4. What role does gravity play in the dynamics of water falling from the side of a tank?

Gravity is the main force at play in the dynamics of water falling from the side of a tank. It is what causes the water to fall in the first place, and its strength can determine the speed and trajectory of the falling water. Gravity also influences the shape of the water as it falls and how it interacts with any external forces, such as air resistance or wind.

5. Can the shape and angle of the tank affect the splash pattern of the falling water?

Yes, the shape and angle of the tank can affect the splash pattern of the falling water. A tank with a wider and flatter opening may create a more spread-out and chaotic splash, while a tank with a narrower and steeper opening may produce a more focused and directed splash. The angle of the tank can also impact the direction and shape of the falling water, as well as the size and shape of the resulting splash.

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