Calculating Water Flow from a Limestone Tube in a Freshwater Pond

In summary, the problem involves a fresh water pond that has eroded a "tube" through a limestone bed, allowing water to emerge on the other side of a cliff. The "tube" has a diameter of 4.26 cm and is located 6.1 m below the surface of the pond. The question asks for the volume of water that flows out of the "tube" in 3.35 hr after a rock blocking the exit is removed. To solve this, Bernoulli's equation and the equation for volume are needed, but the velocity and pressure values are unknown. Further calculations are needed to determine the solution.
  • #1
ashwinanand
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Homework Statement



A fresh water pond that is 15.0 m deep is contained on one side by a cliff. The water has eroded a nearly horizontal "tube" through a bed of limestone, which allows the water to emerge on the other side of the cliff. If the "tube" has a diameter of 4.26 cm, and is located 6.1 m below the surface of the pond. The frictional force between the "tube" wall and a rock that is blocking the exit is 85.9N. When the rock is removed, what volume of water flows out of the "tube" in 3.35 hr?


Homework Equations



Volume= velocity*area*time

bernoulli's equation: P+0.5 /rho(v^2)+rho*g*y

The Attempt at a Solution



P1+0.5(1000kg/m^3)(v1^2)+(1000)(9.8m/s^2)(6.1m) = P2+0.5(1000kg/m^3)(v2^2)+(1000)(9.8m/s^2)(6.1m)

I am confused on how to find velocity. I know bernoulli's equation needs to be used but would I use 6.1m for both sides and how do I solve for velocities when I have two unknown velocities and don't know Pressure.
 
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  • #2
Should I use the equation for Volume to solve for velocity or should I be using Bernoulli's equation?
 

Related to Calculating Water Flow from a Limestone Tube in a Freshwater Pond

1. What is fluid dynamics?

Fluid dynamics is a branch of physics that studies the movement and behavior of fluids, which includes liquids and gases. It involves studying the forces and motions of fluids in various situations, such as in pipes, around objects, and within different environments.

2. What are the main principles of fluid dynamics?

The main principles of fluid dynamics are based on the laws of conservation of mass, momentum, and energy. These principles help us understand how fluids behave and interact with their surroundings, and are the foundation for many practical applications in engineering and science.

3. How is fluid dynamics used in the real world?

Fluid dynamics has a wide range of applications in the real world, including in industries such as aerospace, automotive, and marine engineering. It is used to design and optimize the performance of various systems, such as aircraft wings, car engines, and ship hulls. It also plays a crucial role in understanding weather patterns, ocean currents, and blood flow in the human body.

4. What are some important equations in fluid dynamics?

Some important equations in fluid dynamics include the Navier-Stokes equations, which describe the motion of a fluid in terms of its velocity, pressure, and density; the Bernoulli's equation, which relates the speed of a fluid to its pressure; and the continuity equation, which states that the mass flow rate of a fluid remains constant in a closed system.

5. What are the major challenges in studying fluid dynamics?

One of the major challenges in studying fluid dynamics is the complexity of the equations that govern fluid behavior. These equations often have to be solved numerically, which requires significant computational power and resources. Another challenge is accurately modeling and predicting turbulent flow, which is a chaotic and unpredictable type of fluid motion that occurs in many real-world situations.

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