Re: A question of efficiency

rfellows00@xxxxxxxxx wrote:

I been reading here for a few weeks. All else held constant and
comparing apples to apples...If your goal is to have maximum wind speed
over a controlled cubic area within a cylinder and your biggest
constraint is cost of electricity consumed, would you "push" the air
through the controlled area from a blower at the entrance of the
cylinder OR "pull" the air through from a blower at the exit.
Thank you in advance. Ronnie

I thought there would be more discussion on this post:

Analysis:

System A 'pulling'

P1 P3 P1
---------------------------------
/\ ^ <--
/ \ | <--
\ / | <--
|| |D QA = Q <-- vA
/ \ | <--
\ / | <--
\/ v <--
---------------------------------
<- L ->



System B 'pushing'

P1 P3 P1
---------------------------------
^ <-- /\
| <-- / \
| <-- \ /
QB = Q |D <-- vB ||
| <-- / \
| <-- \ /
v <-- \/
---------------------------------
<- L ->


Governing equations:

1. vA is average velocity in System A 'pulling' volume (V)

2. vB is average velocity in System B 'pushing' volume (V)

2. P2 - P1 = rhoB (L / D) vB^2 / 2

3. P1 - P3 = rhoA (L / D) vA^2 / 2

4. V = (pi / 4) D^2 L (V is Volume where VA = VB)

5. P V = n R T (air compressiblity
or expandibility)
or

P = (n / V) R T = (rho / M) R T

6. Power = P Q (Q is flowrate and QA = QB)

Therefore:

rho = (P1 + P2)/2 M / (R T)

and

P2 - P1 = (P1 + P2)/2 M / (R T) (L / D) vB^2 / 2
= (P1 + P2) k vB^2
and

P1 - P3 = (P1 + P3)/2 M / (R T) (L / D) vB^2 / 2
= (P1 + P3) k vA^2

rearrange:

k vB^2 = (P2 - P1)/ (P1 + P2)

k vA^2 = (P1 - P3)/ (P1 + P3)

As defined:

P2 > P1 > P3

let for example:

k = 1 P1 = 10 P2 = 11 P3 = 9

then:

vB^2 = (11 - 10)/ (10 + 11) = 1/21

vA^2 = (10 - 9)/ (10 + 9) = 1/19

therefore:

vA > vB

Due to air expandibility
Condition A 'pulling' results in faster velocity vA
than air compressiblity
Condition B 'pushing' resulting in slower velocity vB

The power is the same for A and B
Power = (P2 - P1) Q = (P1 - P3) Q

but 'power / mass' in volume 'V'
is just the opposite of 'power / velocity'.

power/(rhoA V) > power/(rhoB V)

Richard Saam







.

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