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Discussing a Bernoulli Problem

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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Solution Preview

Please refer to the attachment.

Problem:

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)

Solution:
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)
Where
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 ...

Solution Summary

This solution is comprised of a very thorough, step by step explanation, which clearly illustrates how to solve the following problem. All the equations and variables needed are explained and using this solution, one should have a clear understanding of what each variable means. In order to view the solution, a Word document needs to be opened.

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