How Does Water Flow Dynamics Work in a Tank System?

In summary, the problem presents an open tank with water flowing steadily from it. The elevation of point 1 is 10.0 m and the elevations of points 2 and 3 are 2.00 m. The cross-sectional area at point 2 is 4.80 x 10^-2 m^2 and at point 3, where the water is discharged, it is 1.60 x 10^-2 m^2. The cross-sectional area of the tank is much larger than the pipe. The task is to use Bernoulli's equation to compute the volume of water DeltaV that flows across the exit of the pipe in 1.00 s.
  • #1
av8tor
2
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Homework Statement



Link to picture: http://session.masteringphysics.com/problemAsset/1011222/12/yf_Figure_14_41.jpg

Water flows steadily from an open tank as shown in the figure. The elevation of point 1 is 10.0 m, and the elevation of points 2 and 3 is 2.00 m. The cross-sectional area at point 2 is 4.80×10−2 m^2; at point 3, where the water is discharged, it is 1.60×10−2 m^2. The cross-sectional area of the tank is very large compared with the cross-sectional area of the pipe.


Homework Equations



Delta V = (A)(v)( Delta t)

A1(v)1=A2(v)2

The Attempt at a Solution



I can't figure this out.

To know the velocity of at point 3, don't you have to know the area of the main tank, to get the velocity at point 2, and then point 3?

The Area of point 2 and 3 is given, but no velocity, so what am I missing??
 
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  • #2
So it ask:

Assuming that Bernoulli's equation applies, compute the volume of water DeltaV that flows across the exit of the pipe in 1.00 {\rm s}. In other words, find the discharge rate \Delta V/\Delta t.
 
  • #3


I would first clarify any uncertainties or missing information in the given problem. In this case, it seems that the velocity at points 2 and 3 is not provided, which is necessary to solve the problem. Additionally, the specific units for the cross-sectional areas are not given, which could affect the calculations. I would also suggest checking the given values and equations to ensure they are consistent and appropriate for the problem.

Assuming that the given values are accurate and the equation for continuity (A1v1 = A2v2) is applicable, we can solve for the velocity at point 3 by setting the cross-sectional areas and velocities at points 1 and 2 equal to each other. This will give us the velocity at point 2, which can then be used to solve for the velocity at point 3.

Alternatively, if the tank is open to the atmosphere and the water is flowing out of it, we can use the equation for Bernoulli's principle (P1 + 1/2ρv1^2 + ρgh1 = P2 + 1/2ρv2^2 + ρgh2) to solve for the velocity at point 3. This equation takes into account the pressure and elevation differences between points 1 and 2, along with the velocity of the water at each point.

In either case, it is important to carefully consider the given information and use appropriate equations to solve for the unknown variables.
 

Related to How Does Water Flow Dynamics Work in a Tank System?

What is water flow?

Water flow refers to the movement of water from one place to another, typically due to gravity or pressure differences.

What factors affect water flow?

The rate of water flow can be affected by various factors such as the size and shape of the tank, the pressure of the water, the opening through which the water flows, and the viscosity of the water.

How can the flow rate of water be calculated?

The flow rate of water can be calculated using the formula Q = A * V, where Q is the flow rate, A is the cross-sectional area of the tank or opening, and V is the velocity of the water.

What is the difference between laminar and turbulent flow?

Laminar flow is a smooth, orderly movement of water in a single direction, while turbulent flow is chaotic and irregular, with water moving in different directions and creating eddies and swirls.

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

The flow of water from a tank can be controlled by adjusting the pressure or the size of the opening through which the water flows. Other methods include using valves or pumps to regulate the flow.

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