[Rob Wilk]

I did a Civil Engineering course some years ago and from my textbook I had a question on damper blades, which is shown in the 2 attached images.

I'm not sure how to solve this question.

If someone knows may you please explain to me how I should work this out or at least give me some idea where to start ?



https://i.stack.imgur.com/4AMmV.png

[LuckyTran]

Calculate the boundary layer thickness at the end a 200 mm plate and multiply by 2 (b/c parallel blades). Then figure out what % of the plate separation this corresponds to.

[Rob Wilk]

Originally Posted by LuckyTran

Calculate the boundary layer thickness at the end a 200 mm plate and multiply by 2 (b/c parallel blades). Then figure out what % of the plate separation this corresponds to.

Using that velocity profile, I have calculated the boundary layer thickness from formula in my textbook.

Boundary Layer thickness = 5.48 (Rex)^-0.5 * x^0.5

Boundary Layer thickness = 5.48 (mu / (Rho * velocity))^0.5 * x^0.5

Boundary Layer thickness = 5.48 (0.000018 / (1.18 * 25))^0.5 * 0.2^0.5
Boundary Layer thickness = 0.00191434761 m

You say multiply by 2 because there are parallel blades, so we now have
0.0038287 m

You then say "figure out what % of the plate separation this corresponds to".

What is the plate separation, is it 0.2 * 2 = 0.4 m ?

So is this (0.0038287 / 0.4) *100 = 0.957 %

The answer is 0.638 %

I am out, why is this ?

[LuckyTran]

I misread the problem, it's way simpler. I thought the blades were 200 mm long They are not. The plate separation distance is 200 mm. The velocity profile is given. You just need to figure out mean flow thru the gap. Sort of like figuring out the displacement thickness.


If you figure out the correct boundary layer thicknes (the value for delta) and then do a certain integral with the velocity profile you can get the answer in one line.

[Rob Wilk]

Originally Posted by LuckyTran

I misread the problem, it's way simpler. I thought the blades were 200 mm long They are not. The plate separation distance is 200 mm. The velocity profile is given. You just need to figure out mean flow thru the gap. Sort of like figuring out the displacement thickness.


If you figure out the correct boundary layer thicknes (the value for delta) and then do a certain integral with the velocity profile you can get the answer in one line.

I worked out the boundary layer thickness like so:

Boundary Layer thickness = 5.48 (Rex)^-0.5 * x^0.5

Boundary Layer thickness = 5.48 (mu / (Rho * velocity))^0.5 * x^0.5

Boundary Layer thickness = 5.48 (0.000018 / (1.18 * 25))^0.5 * 0.2^0.5
Boundary Layer thickness = 0.00191434761 m

As for the flow through the gap, wouldn't that be the air velocity 25 m/s * 0.2m separation between damper blades * height (what is that)

You mentioned you can get answer in one line by doing integral on velocity profile.

I don't have a way to show the symbols, but I'll explain

So would that be an integral for

2 (y / boundary layer thickness) - (y / boundary layer thickness) ^2

what would y be and what would be the limits for the integral ?


Are you able to please clarify these things that I have mentioned ?

[Rob Wilk]

Originally Posted by LuckyTran

I misread the problem, it's way simpler. I thought the blades were 200 mm long They are not. The plate separation distance is 200 mm. The velocity profile is given. You just need to figure out mean flow thru the gap. Sort of like figuring out the displacement thickness.


If you figure out the correct boundary layer thicknes (the value for delta) and then do a certain integral with the velocity profile you can get the answer in one line.

Hi LuckyTran

Just wondering if you saw my last reply.

Just a few couple of important things to sort out to solve this.

[Rob Wilk]

Originally Posted by LuckyTran

I misread the problem, it's way simpler. I thought the blades were 200 mm long They are not. The plate separation distance is 200 mm. The velocity profile is given. You just need to figure out mean flow thru the gap. Sort of like figuring out the displacement thickness.


If you figure out the correct boundary layer thicknes (the value for delta) and then do a certain integral with the velocity profile you can get the answer in one line.

Are you able to please clarify for me what I have mentioned in my previous reply.

[Rob Wilk]

Originally Posted by LuckyTran

I misread the problem, it's way simpler. I thought the blades were 200 mm long They are not. The plate separation distance is 200 mm. The velocity profile is given. You just need to figure out mean flow thru the gap. Sort of like figuring out the displacement thickness.


If you figure out the correct boundary layer thicknes (the value for delta) and then do a certain integral with the velocity profile you can get the answer in one line.

Are you able to show me the process of how the calculations work with these two ways.

I just haven't got my head around how this is calculated just yet.

You mentioned two ways:

• Mean flow thru gap
• and Getting answer in one line