Calculating Distance from Water Level to Stream Impact Point

In summary: Bernouilli equation to determine the speed of water, which will help determine the horizontal speed and distance above the ground. The time it takes to fall to the ground will also be a factor in solving the problem.
  • #1
whereisccguys
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A tank is filled with water to a height H, 26 m. A hole is punched in one of the walls at a depth h = 6.50 m below the water surface (see the figure). What is the distance x from the base of the tank to the point at which the resulting stream strikes the floor?

i knoe the equation to find out the answer is x = 2\sqrt{h(H-h)} but i have really have no idea why, i knoe I'm suppose to use the kinematic equation of rho g h = 1/2 rho v^2 + rho g (H-h)

can any1 explain to me?

thanks
 
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  • #2
whereisccguys said:
A tank is filled with water to a height H, 26 m. A hole is punched in one of the walls at a depth h = 6.50 m below the water surface (see the figure). What is the distance x from the base of the tank to the point at which the resulting stream strikes the floor?

i knoe the equation to find out the answer is x = 2\sqrt{h(H-h)} but i have really have no idea why, i knoe I'm suppose to use the kinematic equation of rho g h = 1/2 rho v^2 + rho g (H-h)
Use the Bernouilli equation to determine the speed, v, of the water. So you will know the horizontal speed and the distance above the ground. That is all you need to solve it. Hint: what is the time it takes to fall to the ground?

AM
 
  • #3
for your question. The equation you mentioned, x = 2\sqrt{h(H-h)}, is derived from the kinematic equation you mentioned, which is used to describe the motion of an object under the influence of gravity. In this case, the object is the water stream coming out of the hole in the tank wall.

To understand this equation, let's break it down. The first part, 2\sqrt{h(H-h)}, represents the distance traveled by the water stream in a free fall. This is because when the water comes out of the hole, it is only under the influence of gravity and will follow a parabolic path. The distance traveled by an object in free fall can be calculated using the equation s = ut + 1/2at^2, where s is the distance traveled, u is the initial velocity (which is zero in this case), a is the acceleration due to gravity, and t is the time taken. In this case, the time taken is the same for both the horizontal and vertical components of the water stream's motion, so we can use the equation s = 1/2at^2. Plugging in the values for acceleration due to gravity (g) and time (t), we get s = 1/2gt^2 = 1/2gh, where h is the height at which the hole is located. This gives us the first part of the equation, 2\sqrt{h(H-h)}.

The second part of the equation, rho g (H-h), represents the distance traveled by the water stream horizontally before it hits the floor. This is because the water stream is also moving horizontally due to the pressure of the water above it (which is represented by rho g (H-h)). The distance traveled horizontally can be calculated using the equation s = vt, where s is the distance traveled, v is the horizontal velocity, and t is the time taken. In this case, the horizontal velocity is the same as the initial horizontal velocity of the water stream, which is zero. So, the equation becomes s = 0t = 0. This means that the distance traveled horizontally is zero, and we can ignore this part of the equation.

Putting these two parts together, we get x = 2\sqrt{h(H-h)} + rho g (H-h). This gives us the distance from the base of the tank to the point where the water stream hits the floor.

I
 

1. How is the distance from water level to stream impact point calculated?

The distance from water level to stream impact point is calculated by subtracting the elevation of the water level from the elevation of the impact point. This will give you the vertical distance between the two points.

2. What tools and measurements are needed to calculate this distance?

To calculate the distance from water level to stream impact point, you will need a topographic map that shows the elevation of both points, a ruler or measuring tape, and a calculator.

3. Can this distance be calculated for any body of water and stream?

Yes, as long as the topographic map has the necessary elevation information for both the water level and the stream impact point, this distance can be calculated for any body of water and stream.

4. What is the importance of calculating this distance?

Calculating the distance from water level to stream impact point can provide valuable information for flood risk assessment, erosion control, and land use planning. It can also help in understanding the impact of human activities on the environment.

5. Are there any limitations to this calculation method?

There may be limitations to this calculation method if the topographic map does not accurately reflect the elevation of the water level or the stream impact point. Additionally, this method does not take into account factors such as water flow and stream velocity, which can affect the actual impact of the stream on the surrounding area.

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