Fluid Dynamics Homework: Solving for Water Speed and Range in a Container

In summary, the conversation discusses the use of Bernoulli's equation to calculate the speed of water from spouts of different heights in a container with a constant water level of 45 cm. The attempt at solving for the spout with a height of 40 cm is shown, with the only error being the incorrect conversion of height from cm to m. The correct solution is 9.9 cm/s. Good luck.
  • #1
azure2s
2
0

Homework Statement



A container has spouts 10 cm, 20 cm, 30 cm, and 40 cm. The water level is maintained at a 45 cm height by an outside supply. (a) what is the speed of the water out of each hole? (b) which water stream has the greatest range relative to the base of the container?

Homework Equations



Bernoulli's Equation: p1 + 1/2desnityv12 + pgy1 = p2 + 1/2densityv22 + pgy2

The Attempt at a Solution



I tried to first solve the the spout 40 cm high. Using the equation, the pressure and density gets canceled, so we have:

v12 - v22 = 2g(y2 - y1)

since v2 = 0, then

v1 = square root of 2g(y2 - y1)

v1 = square root of 2(9.8)(45 - 40)
v1 = 9.9

But my answer is wrong according to my teacher... :( Hope you can help me
 
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  • #2
azure2s said:

Homework Statement



A container has spouts 10 cm, 20 cm, 30 cm, and 40 cm. The water level is maintained at a 45 cm height by an outside supply. (a) what is the speed of the water out of each hole? (b) which water stream has the greatest range relative to the base of the container?

Homework Equations



Bernoulli's Equation: p1 + 1/2desnityv12 + pgy1 = p2 + 1/2densityv22 + pgy2

The Attempt at a Solution



I tried to first solve the the spout 40 cm high. Using the equation, the pressure and density gets canceled, so we have:

v12 - v22 = 2g(y2 - y1)

since v2 = 0, then

v1 = square root of 2g(y2 - y1)

v1 = square root of 2(9.8)(45 - 40)
v1 = 9.9

But my answer is wrong according to my teacher... :( Hope you can help me

Your height difference is measured in cm not m.
 
  • #3
LowlyPion said:
Your height difference is measured in cm not m.

LOL! I can't believe that was the only mistake I did! Thank you very much! =)) Now my answer is the same with my teacher's.
 
  • #4
azure2s said:
LOL! I can't believe that was the only mistake I did! Thank you very much! =)) Now my answer is the same with my teacher's.

Good luck.
 

1. What is Fluid Dynamics?

Fluid Dynamics is the study of how fluids, such as liquids and gases, move and behave under different conditions. It involves understanding the principles of mass, energy, and momentum to analyze and predict the behavior of fluids in various systems.

2. Why is Fluid Dynamics important?

Fluid Dynamics plays a crucial role in many fields such as engineering, meteorology, and oceanography. It helps us understand the behavior of fluids in different environments and allows us to design and optimize systems for various applications such as aircraft, ships, and weather forecasting.

3. Can you give an example of a real-world application of Fluid Dynamics?

One example of a real-world application of Fluid Dynamics is in the design and optimization of airplane wings. Understanding the behavior of air flow over the wings allows engineers to design more efficient and aerodynamic wings, resulting in improved flight performance and fuel efficiency.

4. What are some common equations used in Fluid Dynamics?

Some common equations used in Fluid Dynamics include the Navier-Stokes equations, which describe the motion of fluids, the continuity equation, which represents the conservation of mass, and the Bernoulli's equation, which relates the pressure and velocity of a fluid in motion.

5. How can I improve my understanding of Fluid Dynamics?

To improve your understanding of Fluid Dynamics, you can start by familiarizing yourself with the basic principles and equations. It is also helpful to practice solving problems and conducting experiments to see the concepts in action. Additionally, staying updated on current research and developments in the field can help deepen your understanding and expand your knowledge.

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