# 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).

#### 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

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