Water Flowing From a Tank

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In summary, the water is flowing from an open tank with point 1 at an elevation of 10.0 meters and points 2 and 3 at an elevation of 2.00 meters. The cross-sectional area at point 2 is 0.0480 square meters and at point 3, where the water is discharged, it is 0.0160 square meters. The tank has a much larger cross-sectional area compared to the pipe. To find the discharge rate using Bernoulli's equation, we need to find the other terms in the equation and express the answer in cubic meters per second.
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horsegirl09
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Water flows steadily from an open tank as shown in the figure.The elevation of point 1 is 10.0 meters, and the elevation of points 2 and 3 is 2.00 meters. The cross-sectional area at point 2 is 0.0480 square meters; at point 3, where the water is discharged, it is 0.0160 square meters. The cross-sectional area of the tank is very large compared with the cross-sectional area of the pipe.

Assuming that Bernoulli's equation applies, compute the discharge rate .
Express your answer in cubic meters per second.

I have no idea how to approach this...sorry...any help i can get would be amazing!
 
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  • #2
Write out what you know.
Then write out what you need to find.
Then write down the equations you are using (in this case Bernoulli's Equation and the definition for volume flow rate)

What other terms of the equation do you need to find in order to solve the problem?
 
  • #3


I would approach this problem by first understanding the principles of Bernoulli's equation and how it applies to fluid flow. Bernoulli's equation states that the total energy of a fluid remains constant as it moves through a pipe or open tank.

In this scenario, we know the elevation at points 1, 2, and 3, as well as the cross-sectional areas at points 2 and 3. We can use Bernoulli's equation to calculate the discharge rate by equating the total energy at point 1 to the total energy at point 3.

The total energy at a point is determined by the sum of the potential energy (due to elevation) and the kinetic energy (due to flow velocity). Since the cross-sectional area at point 2 is larger than at point 3, the water will flow faster at point 3, resulting in a higher kinetic energy.

Using the equation P1 + ρgh1 + 1/2ρv1^2 = P3 + ρgh3 + 1/2ρv3^2, where P is the pressure, ρ is the density of water, g is the acceleration due to gravity, h is the elevation, and v is the velocity, we can solve for the velocity at point 3.

Rearranging the equation to solve for v3, we get v3 = √(2gh1 - 2gh3 + v1^2). Plugging in the values given in the problem, we get v3 = √(2(9.8 m/s^2)(10.0 m) - 2(9.8 m/s^2)(2.00 m) + 0^2) = 8.86 m/s.

To calculate the discharge rate, we need to multiply the velocity at point 3 by the cross-sectional area at point 3. This gives us a discharge rate of 8.86 m/s x 0.0160 m^2 = 0.142 m^3/s.

Therefore, the discharge rate of water from the tank is 0.142 cubic meters per second. This means that approximately 0.142 cubic meters of water flows out of the tank every second.
 

1. How does water flow from a tank?

Water flows from a tank due to the force of gravity. When the tank is filled with water, the weight of the water creates pressure at the bottom of the tank. This pressure pushes the water out of the tank and through any connected pipes or channels.

2. What factors affect the rate of water flow from a tank?

The rate of water flow from a tank can be affected by several factors, including the size and shape of the tank, the height of the water level, the size and material of the outlet pipe, and any obstructions or restrictions in the flow path.

3. How can the flow of water from a tank be controlled?

The flow of water from a tank can be controlled by adjusting the height of the water level in the tank, changing the size of the outlet pipe, or installing a valve or gate to regulate the flow. Other methods such as using a pump or changing the angle of the tank can also control the flow.

4. What happens if the outlet pipe from a tank is blocked?

If the outlet pipe from a tank is blocked, the water will not be able to flow out of the tank. This can cause the water level in the tank to rise, potentially leading to overflowing or damage to the tank. It is important to regularly check and maintain the outlet pipe to ensure proper water flow.

5. How does the flow of water from a tank affect the surrounding environment?

The flow of water from a tank can have various impacts on the surrounding environment. It can provide necessary water for plants and animals, contribute to erosion and sedimentation, and affect the water quality of nearby bodies of water. Proper management and control of water flow is important to minimize negative impacts on the environment.

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