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Discussing a Bernoulli Problem

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Please help understanding the effects of a stream which is flowing through a tube. I've prepared the following problem for discussion.

Using Bernoulli's equation and the steady flow momentum relation to calculate the net force on a tube from a dynamic pressure drop and a water flow stream flowing through ta tube.

See the attachment for further detail and calculate the following:

- V1 and V3
- Force pushing tube to the left
- Force pushing tube to the right
- Net force acting on the tube (x dir) and which way it is acting (right or left).

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Please refer to the attachment.


Using Bernoulli's equation and the steady flow momentum relation calculate the net force on a tube from a dynamic pressure drop and a water flow stream flowing through the tube.

See attachment for problem and calculate the following:

1) V1 and V3
2) Force pushing tube to left
3) Force pushing tube to right
4) Net force acting on tube (x dir) and which way (right or left)

1) First of all, I prefer to work in SI units. For convenience, I can convert afterwards in British units too.

Pext = 4500 psi = 310.3 bar
Pa = 14.5 psi = 1 bar
D1 = 1.75 in = 0.044 m
D2 = 2.0 in = 0.051 m
Da = 0.5 in = 0.013 m
V2 = V4 = 802 ft/s = 244.4 m/s

The equations that we need to apply in order to solve the problem are:

Bernoulli's equation between the inlet and outlet of each side tube (which is the same, since V2 = V4):
( 1)
pext = total pressure at the inlet of each side tube
pa = static pressure at the outlet of each side tube and inlet of downward tube
Δp = pressure losses in side tubes, which are the same in both tubes, since
V2 = V4 and ...

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See Also This Related BrainMass Solution

Discussion Question: Use of hypotheses and hypothesis testing

See attached article.

Review the following articles given under your week 1 Articles - Electronic Reserve Readings link, and write a short synopsis (200 -300 words) of the main points and learning takeaways. In your response, refer to your Seward text readings for week 1, to support your analysis.

Hypotheses are the central tool of scientific observation. Because the core method of scientific investigation is the comparison of expectations against observations of the world, scientists need to make clear statements about their expectations. A hypothesis is a concise, falsifiable statement that is subjected to observational testing as part of a scientific investigation.
Scientific research generally starts with a question about the observable world. In the social sciences research questions focus on human behavior—especially behavior related to groups (e.g., communities, countries, or societies). The scientific method says nothing about the origins of these research questions (just as it says nothing about the content of the areas of research). The scientific method simply requires that a scientist state an answer to this question (the hypothesis) that can be tested with observations (hypothesis testing).
There is a bewildering array of potential research questions—and thus hypotheses—in the domain of social science. Hypotheses can focus on expectations about voting behavior, the tendency of nations to go to war, or the factors that contribute to juvenile delinquency or to decisions about where to live (among many, many other hypotheses).
The purpose of the hypothesis is to ease the task of testing an expectation with observations of the world. A good hypothesis, then, is one that is easily tested. The ease of testing contributes to a second key aspect of the scientific method: reproducibility of testing. A clearly worded hypothesis can be tested repeatedly by a scientist and, maybe more important, by other scientists (King, Keohane, and Verba 1994, pp. 28-29).
Consider the following example. A social scientist may hypothesize that smaller class sizes in secondary schools will lead to higher performance on standardized tests. Because it is easy to observe the number of students in a class and the standardized tests scores are also easily observable (though there may be questions of the validity of the test as a measure of "intelligence" or even "academic achievement"), this hypothesis is easy to test. The test itself is also easy to replicate by the original social scientist or by other investigators. The hypothesis is sufficiently clear that any observer would be able to tell whether people in the smaller classes actually performed better on standardized tests. The judgment, then, is not a product of the specific observer but is instead independent of the identity of the scientist (a subject of some controversy that is discussed in a later section).

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