Hydraulic problem , Water Main

[mcgiiver]

This is not a homework problem, just a discussion problem between engineers,. I would like to see what anwers others get.

Given: A 24 inch diameter water main is operating at 40 lbs/sq. in.. A small hole is drilled in the top of the water main (not buried).

Find: To what height will the water shoot?


That's all the given info you get, make reasonable assumptions as needed.

 

[berkeman]

This is not a homework problem, just a discussion problem between engineers,. I would like to see what anwers others get.

Given: A 24 inch diameter water main is operating at 40 lbs/sq. in.. A small hole is drilled in the top of the water main (not buried).

Find: To what height will the water shoot?


That's all the given info you get, make reasonable assumptions as needed.

Doesn't matter if it's homework or now, you need to show your own work first. What equations and factors did you use? What answer did you get?

 

[russ_watters]

Hint: it's a surprisingly easy question.

 

[mcgiiver]

Hint: it's a surprisingly easy question.

On the surface it seems like a very easy question, it might not be a three term equation.

Is it a hydraulic problem or a ballistic problem. I think both are involved.

 

[PJC01]

I would approach this hydraulic problem by first considering the basic principles of fluid dynamics and Bernoulli's equation. Bernoulli's equation states that the total pressure of a fluid at any point is equal to the sum of its static pressure and dynamic pressure. In this case, the static pressure would be the pressure exerted by the water main at 40 lbs/sq. in., and the dynamic pressure would be the pressure exerted by the water as it flows out of the hole.

Assuming the water main is filled to the top, the height of the water column can be calculated using the equation P = ρgh, where P is the pressure, ρ is the density of water, g is the acceleration due to gravity, and h is the height of the water column. Rearranging the equation to solve for h, we get h = P/(ρg).

Using the given information, we can calculate the height of the water column as follows:

h = (40 lbs/sq. in.)/(62.4 lbs/ft^3 * 32.2 ft/s^2) = 0.0203 ft or 0.24 inches.

This means that the water will shoot out of the hole to a height of approximately 0.24 inches. However, this calculation assumes that the water is flowing out of the hole at a steady rate and that there are no other external factors affecting the flow. In reality, the height of the water column may be slightly lower due to factors such as friction and turbulence.

Additionally, it is important to consider the size of the hole and the flow rate of the water. A smaller hole will result in a higher velocity and thus a higher dynamic pressure, leading to a higher water column height. Similarly, a larger flow rate will also result in a higher velocity and pressure, resulting in a higher water column height.

In conclusion, while the given information is limited, using basic principles of fluid dynamics and making reasonable assumptions, we can estimate that the water will shoot out of the hole to a height of approximately 0.24 inches. However, it is important to keep in mind that this is just an estimate and the actual height may vary depending on various factors. Further analysis and experimentation may be needed to obtain a more accurate answer.