How Deep is the Water in the Tank if Two Streams Hit the Same Spot?

In summary, the conversation discusses a water tank with two holes at different heights and its relation to Bernoulli's equation and projectile motion equations. The pressure in the water is related to the kinetic energy and the mean velocity of the water. The initial velocities of the water exiting the holes can be calculated using Newton's equations of motion, but there can be more than one correct answer for the mean velocity. It is also questioned if the pressure on both holes is equal since they are both open to the atmosphere.
  • #1
Ed Quanta
297
0
A water tank is open to the atmosphere and has two holes in it, one .80 m and one 3.6 m above the floor on which the tank rests. If the two streams of water strikes the floor in the same place, what is the depth of water in the tank? (Assume that the holes are very small and the tank is very large and the top surface of the water has essentially zero speed)

Any help would be appreciated. Thank you.
 
Physics news on Phys.org
  • #2
Ed Quanta said:
A water tank is open to the atmosphere and has two holes in it, one .80 m and one 3.6 m above the floor on which the tank rests. If the two streams of water strikes the floor in the same place, what is the depth of water in the tank? (Assume that the holes are very small and the tank is very large and the top surface of the water has essentially zero speed)

Any help would be appreciated. Thank you.
The water leaves the tank opening at an initial horizontal speed (which is greater at the bottom hole) but with no initial vertical speed. Are you familiar with the projectile motion equations AND Toricelli's Theorem?
 
  • #3
No, I am not. Only Bernoulli's equation
 
  • #4
I'd understand how to set this up if there was only one hole from which water exists the tank, but there are two holes. Anyone know how to apply Bernoulli to this?
 
  • #5
The pressure in the water is a function of depth of water above that point. The pressure can be related to kinetic energy of the water, which is proportional to the square of the mean velocity (speed) of the water from the nozzle.

Think of the relationship between 'gh' and 'v2/2' where g is the acceleration of gravity, h is the height of water, and v is the mean speed of the water issuing from the holes.

Assume the water has a constant lateral velocity and accelerates downward (falls) with gravity.
 
  • #6
Thanks, this helping me a lot. But here is what is bothering me. I can calculate how long it will take for the water exiting each hole to hit the ground using Newton's equations of motion. But all that is required is that the water exiting both holes cover the same horizontal distance. So the initial velocity exiting the bottom hole will be greater than that of the top hole. But isn't there more than one pair of initial velocities that can be selected such that both water streams will hit at the same point? Can't there be more than one correct answer for the mean velocity as a result given the information provided?


Another question I have is this. Is the pressure on both holes equal since both are open to the atmosphere?
 

1. What is fluid mechanics?

Fluid mechanics is a branch of physics that studies the behavior of fluids (liquids and gases) under various conditions, such as flow, pressure, and temperature.

2. What are some practical applications of fluid mechanics?

Fluid mechanics has many practical applications, including designing and optimizing aircraft wings, creating more efficient engines and turbines, understanding weather patterns, and developing medical devices like ventilators.

3. What is the difference between a liquid and a gas in terms of fluid mechanics?

In fluid mechanics, liquids and gases are both considered fluids, but they have different properties. Liquids are generally incompressible, meaning they cannot be easily squeezed into a smaller volume, while gases are compressible and can be easily compressed into a smaller volume.

4. How does Bernoulli's principle relate to fluid mechanics?

Bernoulli's principle states that as the speed of a fluid increases, the pressure decreases. This principle is important in fluid mechanics as it helps explain the lift force on airplane wings, the flow of fluids through pipes, and other phenomena.

5. What is the difference between laminar and turbulent flow?

In fluid mechanics, laminar flow refers to smooth, orderly flow of fluids, while turbulent flow is characterized by chaotic, irregular motion. Laminar flow is typically observed at low velocities and in small pipes, while turbulent flow is more common at higher velocities and in larger pipes.

Similar threads

Replies
50
Views
3K
  • Introductory Physics Homework Help
Replies
6
Views
1K
  • Introductory Physics Homework Help
Replies
17
Views
3K
  • Introductory Physics Homework Help
Replies
6
Views
3K
  • Introductory Physics Homework Help
Replies
1
Views
2K
Replies
11
Views
4K
  • Introductory Physics Homework Help
Replies
3
Views
1K
  • Engineering and Comp Sci Homework Help
2
Replies
49
Views
2K
  • Introductory Physics Homework Help
Replies
18
Views
3K
  • Mechanical Engineering
Replies
22
Views
1K
Back
Top